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2026-01-01
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<p>Last updated on<strong>September 24, 2025</strong></p>
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<p>Last updated on<strong>September 24, 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 items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 84 and 128.</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 items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 84 and 128.</p>
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<h2>What is the GCF of 84 and 128?</h2>
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<h2>What is the GCF of 84 and 128?</h2>
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<p>The<a>greatest common factor</a><a>of</a>84 and 128 is 4. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number.</p>
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<p>The<a>greatest common factor</a><a>of</a>84 and 128 is 4. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number.</p>
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<p>If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because a divisor is always positive.</p>
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<p>If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because a divisor is always positive.</p>
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<h2>How to find the GCF of 84 and 128?</h2>
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<h2>How to find the GCF of 84 and 128?</h2>
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<p>To find the GCF of 84 and 128, a few methods are described below </p>
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<p>To find the GCF of 84 and 128, 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><h3>GCF of 84 and 128 by Using Listing of Factors</h3>
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</ul><h3>GCF of 84 and 128 by Using Listing of Factors</h3>
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<p>Steps to find the GCF of 84 and 128 using the listing of<a>factors</a>:</p>
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<p>Steps to find the GCF of 84 and 128 using the listing of<a>factors</a>:</p>
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<p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Factors of 128 = 1, 2, 4, 8, 16, 32, 64, 128.</p>
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<p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Factors of 128 = 1, 2, 4, 8, 16, 32, 64, 128.</p>
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<p><strong>Step 2:</strong>Now, identify the<a>common factors</a>Common factors of 84 and 128: 1, 2, 4.</p>
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<p><strong>Step 2:</strong>Now, identify the<a>common factors</a>Common factors of 84 and 128: 1, 2, 4.</p>
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<p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 4. The GCF of 84 and 128 is 4.</p>
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<p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 4. The GCF of 84 and 128 is 4.</p>
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<h3>GCF of 84 and 128 Using Prime Factorization</h3>
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<h3>GCF of 84 and 128 Using Prime Factorization</h3>
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<p>To find the GCF of 84 and 128 using the Prime Factorization Method, follow these steps:</p>
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<p>To find the GCF of 84 and 128 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 Prime Factors of 84: 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7 Prime Factors of 128: 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁷</p>
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<p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 84: 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7 Prime Factors of 128: 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁷</p>
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<p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 × 2 = 2²</p>
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<p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 × 2 = 2²</p>
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<p><strong>Step 3:</strong>Multiply the common prime factors 2² = 4. The Greatest Common Factor of 84 and 128 is 4.</p>
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<p><strong>Step 3:</strong>Multiply the common prime factors 2² = 4. The Greatest Common Factor of 84 and 128 is 4.</p>
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<h3>GCF of 84 and 128 Using Division Method or Euclidean Algorithm Method</h3>
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<h3>GCF of 84 and 128 Using Division Method or Euclidean Algorithm Method</h3>
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<p>Find the GCF of 84 and 128 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 128 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 128 by 84 128 ÷ 84 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 128 - (84×1) = 44 The remainder is 44, not zero, so continue the process</p>
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<p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 128 by 84 128 ÷ 84 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 128 - (84×1) = 44 The remainder is 44, not zero, so continue the process</p>
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<p><strong>Step 2:</strong>Now divide the previous divisor (84) by the previous remainder (44) Divide 84 by 44 84 ÷ 44 = 1 (quotient), remainder = 84 - (44×1) = 40</p>
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<p><strong>Step 2:</strong>Now divide the previous divisor (84) by the previous remainder (44) Divide 84 by 44 84 ÷ 44 = 1 (quotient), remainder = 84 - (44×1) = 40</p>
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<p><strong>Step 3:</strong>Continue dividing 44 ÷ 40 = 1 (quotient), remainder = 44 - (40×1) = 4</p>
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<p><strong>Step 3:</strong>Continue dividing 44 ÷ 40 = 1 (quotient), remainder = 44 - (40×1) = 4</p>
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<p><strong>Step 4:</strong>Divide 40 by 4 40 ÷ 4 = 10 (quotient), remainder = 40 - (4×10) = 0 The remainder is zero, so the divisor will become the GCF.</p>
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<p><strong>Step 4:</strong>Divide 40 by 4 40 ÷ 4 = 10 (quotient), remainder = 40 - (4×10) = 0 The remainder is zero, so the divisor will become the GCF.</p>
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<p>The GCF of 84 and 128 is 4.</p>
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<p>The GCF of 84 and 128 is 4.</p>
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<h2>Common Mistakes and How to Avoid Them in GCF of 84 and 128</h2>
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<h2>Common Mistakes and How to Avoid Them in GCF of 84 and 128</h2>
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<p>Finding the GCF of 84 and 128 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 128 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 gardener has 84 tulips and 128 roses. She wants to plant them in rows with the largest possible number of flowers in each row. How many flowers will be in each row?</p>
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<p>A gardener has 84 tulips and 128 roses. She wants to plant them in rows with the largest possible number of flowers in each row. How many flowers will be in each row?</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 128. GCF of 84 and 128 2² = 4. There are 4 flowers in each row. 84 ÷ 4 = 21 128 ÷ 4 = 32 There will be 4 rows, with each row containing 21 tulips and 32 roses.</p>
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<p>We should find the GCF of 84 and 128. GCF of 84 and 128 2² = 4. There are 4 flowers in each row. 84 ÷ 4 = 21 128 ÷ 4 = 32 There will be 4 rows, with each row containing 21 tulips and 32 roses.</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 128 is 4, the gardener can make rows with 4 flowers each.</p>
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<p>As the GCF of 84 and 128 is 4, the gardener can make rows with 4 flowers each.</p>
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<p>Now divide 84 and 128 by 4.</p>
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<p>Now divide 84 and 128 by 4.</p>
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<p>Each row will have 21 tulips and 32 roses.</p>
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<p>Each row will have 21 tulips and 32 roses.</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 school has 84 desks and 128 chairs. They want to arrange them in groups with the same number of desks and chairs in each group, using the greatest possible number of items per group. How many items will be in each group?</p>
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<p>A school has 84 desks and 128 chairs. They want to arrange them in groups with the same number of desks and chairs in each group, using the greatest possible number of items per group. How many items will be in each group?</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 128 2² = 4. So each group will have 4 items.</p>
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<p>GCF of 84 and 128 2² = 4. So each group will have 4 items.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>There are 84 desks and 128 chairs.</p>
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<p>There are 84 desks and 128 chairs.</p>
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<p>To find the total number of items in each group, we should find the GCF of 84 and 128.</p>
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<p>To find the total number of items in each group, we should find the GCF of 84 and 128.</p>
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<p>There will be 4 items in each group.</p>
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<p>There will be 4 items in each group.</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 128 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 128 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 128. The GCF of 84 and 128 2² = 4. The fabric pieces are 4 meters long.</p>
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<p>For calculating the longest equal length, we have to calculate the GCF of 84 and 128. The GCF of 84 and 128 2² = 4. The fabric pieces are 4 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 each fabric piece, first we need to calculate the GCF of 84 and 128, which is 4.</p>
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<p>For calculating the longest length of each fabric piece, first we need to calculate the GCF of 84 and 128, which is 4.</p>
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<p>The length of each piece of fabric will be 4 meters.</p>
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<p>The length of each piece of fabric will be 4 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 128 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 128 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 128 2² = 4. The longest length of each piece is 4 cm.</p>
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<p>The carpenter needs the longest piece of wood. GCF of 84 and 128 2² = 4. The longest length of each piece is 4 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 128 cm, respectively, we have to find the GCF of 84 and 128, which is 4 cm.</p>
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<p>To find the longest length of each piece of the two wooden planks, 84 cm and 128 cm, respectively, we have to find the GCF of 84 and 128, which is 4 cm.</p>
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<p>The longest length of each piece is 4 cm.</p>
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<p>The longest length of each piece is 4 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 4, and the LCM is 2688, find ‘b’.</p>
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<p>If the GCF of 84 and ‘b’ is 4, and the LCM is 2688, 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 128.</p>
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<p>The value of ‘b’ is 128.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>GCF × LCM = product of the numbers</p>
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<p>GCF × LCM = product of the numbers</p>
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<p>4 × 2688 = 84 × b</p>
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<p>4 × 2688 = 84 × b</p>
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<p>10752 = 84b</p>
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<p>10752 = 84b</p>
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<p>b = 10752 ÷ 84</p>
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<p>b = 10752 ÷ 84</p>
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<p>= 128</p>
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<p>= 128</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 128</h2>
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<h2>FAQs on the Greatest Common Factor of 84 and 128</h2>
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<h3>1.What is the LCM of 84 and 128?</h3>
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<h3>1.What is the LCM of 84 and 128?</h3>
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<p>The LCM of 84 and 128 is 2688.</p>
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<p>The LCM of 84 and 128 is 2688.</p>
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<h3>2.Is 128 divisible by 2?</h3>
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<h3>2.Is 128 divisible by 2?</h3>
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<p>Yes, 128 is divisible by 2 because it is an even number.</p>
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<p>Yes, 128 is divisible by 2 because it is an even number.</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 84?</h3>
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<h3>4.What is the prime factorization of 84?</h3>
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<p>The prime factorization of 84 is 2² × 3 × 7.</p>
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<p>The prime factorization of 84 is 2² × 3 × 7.</p>
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<h3>5.Are 84 and 128 prime numbers?</h3>
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<h3>5.Are 84 and 128 prime numbers?</h3>
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<p>No, 84 and 128 are not prime numbers because both of them have more than two factors.</p>
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<p>No, 84 and 128 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 128</h2>
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<h2>Important Glossaries for GCF of 84 and 128</h2>
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<ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 4 are 1, 2, and 4.</li>
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<ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 4 are 1, 2, and 4.</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 4 are 4, 8, 12, 16, 20, 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 4 are 4, 8, 12, 16, 20, 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 84 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 84 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 44 is divided by 40, the remainder is 4 and the quotient is 1.</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 44 is divided by 40, the remainder is 4 and the quotient is 1.</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 84 and 128 is 2688.</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 84 and 128 is 2688.</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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<p>▶</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>