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2026-01-01
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<p>Last updated on<strong>September 18, 2025</strong></p>
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<p>Last updated on<strong>September 18, 2025</strong></p>
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<p>The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 84 and 56.</p>
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<p>The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 84 and 56.</p>
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<h2>What is the GCF of 84 and 56?</h2>
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<h2>What is the GCF of 84 and 56?</h2>
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<p>The<a>greatest common factor</a>of 84 and 56 is 28. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.</p>
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<p>The<a>greatest common factor</a>of 84 and 56 is 28. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.</p>
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<p>The GCF of two numbers cannot be negative because divisors are always positive.</p>
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<p>The GCF of two numbers cannot be negative because divisors are always positive.</p>
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<h2>How to find the GCF of 84 and 56?</h2>
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<h2>How to find the GCF of 84 and 56?</h2>
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<p>To find the GCF of 84 and 56, a few methods are described below </p>
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<p>To find the GCF of 84 and 56, a few methods are described below </p>
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<ul><li>Listing Factors </li>
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<ul><li>Listing Factors </li>
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<li>Prime Factorization </li>
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<li>Prime Factorization </li>
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<li>Long Division Method / by Euclidean Algorithm</li>
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<li>Long Division Method / by Euclidean Algorithm</li>
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</ul><h2>GCF of 84 and 56 by Using Listing of factors</h2>
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</ul><h2>GCF of 84 and 56 by Using Listing of factors</h2>
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<p>Steps to find the GCF of 84 and 56 using the listing of<a>factors</a></p>
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<p>Steps to find the GCF of 84 and 56 using the listing of<a>factors</a></p>
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<p><strong>Step 1:</strong>Firstly, list the factors of each number</p>
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<p><strong>Step 1:</strong>Firstly, list the factors of each number</p>
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<p>Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.</p>
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<p>Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.</p>
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<p>Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56.</p>
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<p>Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56.</p>
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<p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 84 and 56: 1, 2, 4, 7, 14, 28.</p>
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<p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 84 and 56: 1, 2, 4, 7, 14, 28.</p>
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<p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 28. The GCF of 84 and 56 is 28.</p>
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<p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 28. The GCF of 84 and 56 is 28.</p>
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<h2>GCF of 84 and 56 Using Prime Factorization</h2>
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<h2>GCF of 84 and 56 Using Prime Factorization</h2>
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<p>To find the GCF of 84 and 56 using the Prime Factorization Method, follow these steps:</p>
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<p>To find the GCF of 84 and 56 using the Prime Factorization Method, follow these steps:</p>
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<p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number</p>
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<p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number</p>
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<p>Prime Factors of 84: 84 = 2 x 2 x 3 x 7 = 2² x 3 x 7</p>
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<p>Prime Factors of 84: 84 = 2 x 2 x 3 x 7 = 2² x 3 x 7</p>
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<p>Prime Factors of 56: 56 = 2 x 2 x 2 x 7 = 2³ x 7</p>
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<p>Prime Factors of 56: 56 = 2 x 2 x 2 x 7 = 2³ x 7</p>
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<p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 x 2 x 7 = 2² x 7</p>
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<p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 x 2 x 7 = 2² x 7</p>
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<p><strong>Step 3:</strong>Multiply the common prime factors 2² x 7 = 4 x 7 = 28. The Greatest Common Factor of 84 and 56 is 28.</p>
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<p><strong>Step 3:</strong>Multiply the common prime factors 2² x 7 = 4 x 7 = 28. The Greatest Common Factor of 84 and 56 is 28.</p>
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<h2>GCF of 84 and 56 Using Division Method or Euclidean Algorithm Method</h2>
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<h2>GCF of 84 and 56 Using Division Method or Euclidean Algorithm Method</h2>
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<p>Find the GCF of 84 and 56 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>
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<p>Find the GCF of 84 and 56 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>
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<p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 84 by 56 84 ÷ 56 = 1 (<a>quotient</a>),</p>
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<p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 84 by 56 84 ÷ 56 = 1 (<a>quotient</a>),</p>
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<p>The<a>remainder</a>is calculated as 84 - (56×1) = 28</p>
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<p>The<a>remainder</a>is calculated as 84 - (56×1) = 28</p>
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<p>The remainder is 28, not zero, so continue the process</p>
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<p>The remainder is 28, not zero, so continue the process</p>
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<p><strong>Step 2:</strong>Now divide the previous divisor (56) by the previous remainder (28) Divide 56 by 28 56 ÷ 28 = 2 (quotient), remainder = 56 - (28×2) = 0</p>
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<p><strong>Step 2:</strong>Now divide the previous divisor (56) by the previous remainder (28) Divide 56 by 28 56 ÷ 28 = 2 (quotient), remainder = 56 - (28×2) = 0</p>
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<p>The remainder is zero, the divisor will become the GCF.</p>
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<p>The remainder is zero, the divisor will become the GCF.</p>
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<p>The GCF of 84 and 56 is 28.</p>
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<p>The GCF of 84 and 56 is 28.</p>
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<h2>Common Mistakes and How to Avoid Them in GCF of 84 and 56</h2>
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<h2>Common Mistakes and How to Avoid Them in GCF of 84 and 56</h2>
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<p>Finding the GCF of 84 and 56 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>
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<p>Finding the GCF of 84 and 56 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>A baker has 84 chocolate cookies and 56 vanilla cookies. He wants to pack them into equal boxes with the largest number of cookies in each box. How many cookies will be in each box?</p>
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<p>A baker has 84 chocolate cookies and 56 vanilla cookies. He wants to pack them into equal boxes with the largest number of cookies in each box. How many cookies will be in each box?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>We should find the GCF of 84 and 56 GCF of 84 and 56 2² x 7 = 4 x 7 = 28.</p>
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<p>We should find the GCF of 84 and 56 GCF of 84 and 56 2² x 7 = 4 x 7 = 28.</p>
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<p>There are 28 equal boxes 84 ÷ 28 = 3 56 ÷ 28 = 2</p>
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<p>There are 28 equal boxes 84 ÷ 28 = 3 56 ÷ 28 = 2</p>
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<p>There will be 28 boxes, and each box gets 3 chocolate cookies and 2 vanilla cookies.</p>
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<p>There will be 28 boxes, and each box gets 3 chocolate cookies and 2 vanilla cookies.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>As the GCF of 84 and 56 is 28, the baker can make 28 boxes.</p>
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<p>As the GCF of 84 and 56 is 28, the baker can make 28 boxes.</p>
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<p>Now divide 84 and 56 by 28.</p>
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<p>Now divide 84 and 56 by 28.</p>
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<p>Each box gets 3 chocolate cookies and 2 vanilla cookies.</p>
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<p>Each box gets 3 chocolate cookies and 2 vanilla cookies.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>A florist has 84 roses and 56 tulips. She wants to arrange them in vases with the same number of flowers in each vase, using the largest possible number of flowers per vase. How many flowers will be in each vase?</p>
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<p>A florist has 84 roses and 56 tulips. She wants to arrange them in vases with the same number of flowers in each vase, using the largest possible number of flowers per vase. How many flowers will be in each vase?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>GCF of 84 and 56 2² x 7 = 4 × 7 = 28. So each vase will have 28 flowers.</p>
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<p>GCF of 84 and 56 2² x 7 = 4 × 7 = 28. So each vase will have 28 flowers.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>There are 84 roses and 56 tulips.</p>
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<p>There are 84 roses and 56 tulips.</p>
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<p>To find the total number of flowers in each vase, we should find the GCF of 84 and 56.</p>
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<p>To find the total number of flowers in each vase, we should find the GCF of 84 and 56.</p>
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<p>There will be 28 flowers in each vase.</p>
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<p>There will be 28 flowers in each vase.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>A tailor has 84 meters of silk fabric and 56 meters of cotton fabric. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>
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<p>A tailor has 84 meters of silk fabric and 56 meters of cotton fabric. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>For calculating the longest equal length, we have to calculate the GCF of 84 and 56</p>
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<p>For calculating the longest equal length, we have to calculate the GCF of 84 and 56</p>
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<p>The GCF of 84 and 56 2² x 7 = 4 × 7 = 28.</p>
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<p>The GCF of 84 and 56 2² x 7 = 4 × 7 = 28.</p>
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<p>Each piece of fabric is 28 meters long.</p>
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<p>Each piece of fabric is 28 meters long.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 84 and 56 which is 28.</p>
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<p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 84 and 56 which is 28.</p>
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<p>The length of each piece of fabric will be 28 meters.</p>
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<p>The length of each piece of fabric will be 28 meters.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>A carpenter has two wooden planks, one 84 cm long and the other 56 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?</p>
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<p>A carpenter has two wooden planks, one 84 cm long and the other 56 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The carpenter needs the longest piece of wood GCF of 84 and 56 2² x 7 = 4 × 7 = 28.</p>
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<p>The carpenter needs the longest piece of wood GCF of 84 and 56 2² x 7 = 4 × 7 = 28.</p>
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<p>The longest length of each piece is 28 cm.</p>
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<p>The longest length of each piece is 28 cm.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the longest length of each piece of the two wooden planks, 84 cm and 56 cm, respectively, we have to find the GCF of 84 and 56, which is 28 cm.</p>
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<p>To find the longest length of each piece of the two wooden planks, 84 cm and 56 cm, respectively, we have to find the GCF of 84 and 56, which is 28 cm.</p>
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<p>The longest length of each piece is 28 cm.</p>
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<p>The longest length of each piece is 28 cm.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>If the GCF of 84 and ‘b’ is 28, and the LCM is 168. Find ‘b’.</p>
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<p>If the GCF of 84 and ‘b’ is 28, and the LCM is 168. Find ‘b’.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The value of ‘b’ is 56.</p>
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<p>The value of ‘b’ is 56.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>GCF x LCM = product of the numbers</p>
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<p>GCF x LCM = product of the numbers</p>
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<p>28 × 168 = 84 × b</p>
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<p>28 × 168 = 84 × b</p>
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<p>4704 = 84b</p>
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<p>4704 = 84b</p>
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<p>b = 4704 ÷ 84 = 56</p>
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<p>b = 4704 ÷ 84 = 56</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on the Greatest Common Factor of 84 and 56</h2>
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<h2>FAQs on the Greatest Common Factor of 84 and 56</h2>
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<h3>1.What is the LCM of 84 and 56?</h3>
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<h3>1.What is the LCM of 84 and 56?</h3>
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<p>The LCM of 84 and 56 is 168.</p>
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<p>The LCM of 84 and 56 is 168.</p>
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<h3>2.Is 84 divisible by 3?</h3>
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<h3>2.Is 84 divisible by 3?</h3>
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<p>Yes, 84 is divisible by 3 because the<a>sum</a>of its digits (8+4) is 12, which is divisible by 3.</p>
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<p>Yes, 84 is divisible by 3 because the<a>sum</a>of its digits (8+4) is 12, which is divisible by 3.</p>
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<h3>3.What will be the GCF of any two prime numbers?</h3>
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<h3>3.What will be the GCF of any two prime numbers?</h3>
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<p>The common factor of<a>prime numbers</a>is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.</p>
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<p>The common factor of<a>prime numbers</a>is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.</p>
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<h3>4.What is the prime factorization of 56?</h3>
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<h3>4.What is the prime factorization of 56?</h3>
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<p>The prime factorization of 56 is 2³ x 7.</p>
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<p>The prime factorization of 56 is 2³ x 7.</p>
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<h3>5.Are 84 and 56 prime numbers?</h3>
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<h3>5.Are 84 and 56 prime numbers?</h3>
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<p>No, 84 and 56 are not prime numbers because both of them have more than two factors.</p>
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<p>No, 84 and 56 are not prime numbers because both of them have more than two factors.</p>
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<h2>Important Glossaries for GCF of 84 and 56</h2>
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<h2>Important Glossaries for GCF of 84 and 56</h2>
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<ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 28 are 1, 2, 4, 7, 14, and 28.</li>
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<ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 28 are 1, 2, 4, 7, 14, and 28.</li>
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</ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, and so on.</li>
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</ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, and so on.</li>
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</ul><ul><li><strong>Prime Factors:</strong>These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 42 are 2, 3, and 7.</li>
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</ul><ul><li><strong>Prime Factors:</strong>These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 42 are 2, 3, and 7.</li>
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</ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.</li>
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</ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.</li>
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</ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 8 and 12 is 24.</li>
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</ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 8 and 12 is 24.</li>
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</ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 14 and 28 will be 14, as it is their largest common factor that divides the numbers completely.</li>
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</ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 14 and 28 will be 14, as it is their largest common factor that divides the numbers completely.</li>
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</ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>
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</ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>
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<h2>Hiralee Lalitkumar Makwana</h2>
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<h2>Hiralee Lalitkumar Makwana</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.</p>
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<p>Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: She loves to read number jokes and games.</p>
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<p>: She loves to read number jokes and games.</p>