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2026-01-01
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>Last updated on<strong>August 5, 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 16 and 49.</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 16 and 49.</p>
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<h2>What is the GCF of 16 and 49?</h2>
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<h2>What is the GCF of 16 and 49?</h2>
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<p>The<a>greatest common factor</a><a>of</a>16 and 49 is 1. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the numbers. 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 divisors are always positive.</p>
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<p>The<a>greatest common factor</a><a>of</a>16 and 49 is 1. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the numbers. 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 divisors are always positive.</p>
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<h2>How to find the GCF of 16 and 49?</h2>
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<h2>How to find the GCF of 16 and 49?</h2>
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<p>To find the GCF of 16 and 49, a few methods are described below:</p>
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<p>To find the GCF of 16 and 49, 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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</ul><ul><li>Prime Factorization</li>
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</ul><ul><li>Prime Factorization</li>
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</ul><ul><li>Long Division Method / by Euclidean Algorithm</li>
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</ul><ul><li>Long Division Method / by Euclidean Algorithm</li>
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</ul><h3>GCF of 16 and 49 by Using Listing of Factors</h3>
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</ul><h3>GCF of 16 and 49 by Using Listing of Factors</h3>
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<p>Steps to find the GCF of 16 and 49 using the listing of<a>factors</a>:</p>
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<p>Steps to find the GCF of 16 and 49 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 16 = 1, 2, 4, 8, 16.</p>
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<p>Factors of 16 = 1, 2, 4, 8, 16.</p>
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<p>Factors of 49 = 1, 7, 49.</p>
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<p>Factors of 49 = 1, 7, 49.</p>
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<p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them.</p>
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<p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them.</p>
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<p>Common factor of 16 and 49: 1.</p>
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<p>Common factor of 16 and 49: 1.</p>
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<p><strong>Step 3:</strong>Choose the largest factor.</p>
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<p><strong>Step 3:</strong>Choose the largest factor.</p>
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<p>The largest factor that both numbers have is 1.</p>
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<p>The largest factor that both numbers have is 1.</p>
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<p>The GCF of 16 and 49 is 1.</p>
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<p>The GCF of 16 and 49 is 1.</p>
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<h3>GCF of 16 and 49 Using Prime Factorization</h3>
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<h3>GCF of 16 and 49 Using Prime Factorization</h3>
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<p>To find the GCF of 16 and 49 using the Prime Factorization Method, follow these steps:</p>
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<p>To find the GCF of 16 and 49 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 16: 16 = 2 x 2 x 2 x 2 = 24</p>
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<p>Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 24</p>
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<p>Prime Factors of 49: 49 = 7 x 7 = 72</p>
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<p>Prime Factors of 49: 49 = 7 x 7 = 72</p>
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<p><strong>Step 2:</strong>Now, identify the common prime factors. There are no common prime factors.</p>
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<p><strong>Step 2:</strong>Now, identify the common prime factors. There are no common prime factors.</p>
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<p><strong>Step 3:</strong>Since there are no common prime factors, the GCF is 1.</p>
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<p><strong>Step 3:</strong>Since there are no common prime factors, the GCF is 1.</p>
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<p>The Greatest Common Factor of 16 and 49 is 1.</p>
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<p>The Greatest Common Factor of 16 and 49 is 1.</p>
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<h3>GCF of 16 and 49 Using Division Method or Euclidean Algorithm Method</h3>
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<h3>GCF of 16 and 49 Using Division Method or Euclidean Algorithm Method</h3>
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<p>Find the GCF of 16 and 49 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>
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<p>Find the GCF of 16 and 49 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.</p>
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<p><strong>Step 1:</strong>First, divide the larger number by the smaller number.</p>
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<p>Here, divide 49 by 16 49 ÷ 16 = 3 (<a>quotient</a>), The<a>remainder</a>is calculated as 49 - (16×3) = 1</p>
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<p>Here, divide 49 by 16 49 ÷ 16 = 3 (<a>quotient</a>), The<a>remainder</a>is calculated as 49 - (16×3) = 1</p>
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<p>The remainder is 1, not zero, so continue the process</p>
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<p>The remainder is 1, not zero, so continue the process</p>
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<p><strong>Step 2:</strong>Now divide the previous divisor (16) by the previous remainder (1)</p>
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<p><strong>Step 2:</strong>Now divide the previous divisor (16) by the previous remainder (1)</p>
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<p>Divide 16 by 1 16 ÷ 1 = 16 (quotient), remainder = 0</p>
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<p>Divide 16 by 1 16 ÷ 1 = 16 (quotient), remainder = 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 16 and 49 is 1.</p>
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<p>The GCF of 16 and 49 is 1.</p>
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<h2>Common Mistakes and How to Avoid Them in GCF of 16 and 49</h2>
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<h2>Common Mistakes and How to Avoid Them in GCF of 16 and 49</h2>
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<p>Finding GCF of 16 and 49 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 GCF of 16 and 49 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 16 rose bushes and 49 tulip bulbs. She wants to plant them in rows with the largest number of plants in each row. How many plants will be in each row?</p>
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<p>A gardener has 16 rose bushes and 49 tulip bulbs. She wants to plant them in rows with the largest number of plants in each row. How many plants 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 16 and 49 GCF of 16 and 49 is 1. There will be 1 plant in each row.</p>
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<p>We should find the GCF of 16 and 49 GCF of 16 and 49 is 1. There will be 1 plant in each row.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>As the GCF of 16 and 49 is 1, the gardener can only plant 1 plant in each row.</p>
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<p>As the GCF of 16 and 49 is 1, the gardener can only plant 1 plant in each row.</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 chef has 16 apples and 49 oranges. He wants to arrange them in baskets with an equal number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?</p>
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<p>A chef has 16 apples and 49 oranges. He wants to arrange them in baskets with an equal number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?</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 16 and 49 is 1. So each basket will have 1 fruit.</p>
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<p>GCF of 16 and 49 is 1. So each basket will have 1 fruit.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>There are 16 apples and 49 oranges.</p>
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<p>There are 16 apples and 49 oranges.</p>
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<p>To find the total number of fruits in each basket, we should find the GCF of 16 and 49.</p>
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<p>To find the total number of fruits in each basket, we should find the GCF of 16 and 49.</p>
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<p>There will be 1 fruit in each basket.</p>
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<p>There will be 1 fruit in each basket.</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 worker has 16 meters of fabric and 49 meters of lace. She wants to cut both materials 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 worker has 16 meters of fabric and 49 meters of lace. She wants to cut both materials 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 16 and 49</p>
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<p>For calculating the longest equal length, we have to calculate the GCF of 16 and 49</p>
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<p>The GCF of 16 and 49 is 1.</p>
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<p>The GCF of 16 and 49 is 1.</p>
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<p>The length of each piece is 1 meter.</p>
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<p>The length of each piece is 1 meter.</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 materials, first we need to calculate the GCF of 16 and 49, which is 1. The length of each piece of material will be 1 meter.</p>
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<p>For calculating the longest length of the materials, first we need to calculate the GCF of 16 and 49, which is 1. The length of each piece of material will be 1 meter.</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 16 cm long and the other 49 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 16 cm long and the other 49 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.</p>
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<p>The carpenter needs the longest piece of wood.</p>
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<p>GCF of 16 and 49 is 1.</p>
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<p>GCF of 16 and 49 is 1.</p>
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<p>The longest length of each piece is 1 cm.</p>
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<p>The longest length of each piece is 1 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, 16 cm and 49 cm, respectively.</p>
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<p>To find the longest length of each piece of the two wooden planks, 16 cm and 49 cm, respectively.</p>
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<p>We have to find the GCF of 16 and 49, which is 1 cm.</p>
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<p>We have to find the GCF of 16 and 49, which is 1 cm.</p>
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<p>The longest length of each piece is 1 cm.</p>
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<p>The longest length of each piece is 1 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 16 and ‘b’ is 1, and the LCM is 784, find ‘b’.</p>
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<p>If the GCF of 16 and ‘b’ is 1, and the LCM is 784, 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 49.</p>
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<p>The value of ‘b’ is 49.</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>1 × 784 = 16 × b</p>
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<p>1 × 784 = 16 × b</p>
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<p>784 = 16b</p>
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<p>784 = 16b</p>
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<p>b = 784 ÷ 16 = 49</p>
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<p>b = 784 ÷ 16 = 49</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 16 and 49</h2>
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<h2>FAQs on the Greatest Common Factor of 16 and 49</h2>
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<h3>1.What is the LCM of 16 and 49?</h3>
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<h3>1.What is the LCM of 16 and 49?</h3>
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<p>The LCM of 16 and 49 is 784.</p>
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<p>The LCM of 16 and 49 is 784.</p>
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<h3>2.Is 16 divisible by 2?</h3>
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<h3>2.Is 16 divisible by 2?</h3>
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<p>Yes, 16 is divisible by 2 because it is an even number.</p>
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<p>Yes, 16 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 49?</h3>
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<h3>4.What is the prime factorization of 49?</h3>
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<p>The prime factorization of 49 is (72).</p>
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<p>The prime factorization of 49 is (72).</p>
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<h3>5.Are 16 and 49 prime numbers?</h3>
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<h3>5.Are 16 and 49 prime numbers?</h3>
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<p>No, 16 and 49 are not prime numbers because both of them have more than two factors.</p>
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<p>No, 16 and 49 are not prime numbers because both of them have more than two factors.</p>
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<h2>Important Glossaries for GCF of 16 and 49</h2>
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<h2>Important Glossaries for GCF of 16 and 49</h2>
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<ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.</li>
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<ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.</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 49 are 7 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 49 are 7 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 49 is divided by 16, 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 49 is divided by 16, 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 16 and 49 is 784.</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 16 and 49 is 784.</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>