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2026-01-01
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<p>Last updated on<strong>September 12, 2025</strong></p>
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<p>Last updated on<strong>September 12, 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 45 and 76.</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 45 and 76.</p>
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<h2>What is the GCF of 45 and 76?</h2>
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<h2>What is the GCF of 45 and 76?</h2>
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<p>The<a>greatest common factor</a>of 45 and 76 is 1. 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. 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>of 45 and 76 is 1. 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. 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 45 and 76?</h2>
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<h2>How to find the GCF of 45 and 76?</h2>
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<p>To find the GCF of 45 and 76, a few methods are described below -</p>
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<p>To find the GCF of 45 and 76, a few methods are described below -</p>
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<ol><li>Listing Factors</li>
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<ol><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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</ol><h2>GCF of 45 and 76 by Using Listing of Factors</h2>
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</ol><h2>GCF of 45 and 76 by Using Listing of Factors</h2>
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<p>Steps to find the GCF of 45 and 76 using the listing of<a>factors</a>:</p>
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<p>Steps to find the GCF of 45 and 76 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 45 = 1, 3, 5, 9, 15, 45. Factors of 76 = 1, 2, 4, 19, 38, 76.</p>
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<p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 45 = 1, 3, 5, 9, 15, 45. Factors of 76 = 1, 2, 4, 19, 38, 76.</p>
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<p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factor of 45 and 76: 1.</p>
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<p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factor of 45 and 76: 1.</p>
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<p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 1. The GCF of 45 and 76 is 1.</p>
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<p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 1. The GCF of 45 and 76 is 1.</p>
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<h2>GCF of 45 and 76 Using Prime Factorization</h2>
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<h2>GCF of 45 and 76 Using Prime Factorization</h2>
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<p>To find the GCF of 45 and 76 using the Prime Factorization Method, follow these steps:</p>
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<p>To find the GCF of 45 and 76 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 45: 45 = 3 × 3 × 5 = 3² × 5</p>
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<p>Prime Factors of 45: 45 = 3 × 3 × 5 = 3² × 5</p>
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<p>Prime Factors of 76: 76 = 2 × 2 × 19 = 2² × 19</p>
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<p>Prime Factors of 76: 76 = 2 × 2 × 19 = 2² × 19</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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<h2>GCF of 45 and 76 Using Division Method or Euclidean Algorithm Method</h2>
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<h2>GCF of 45 and 76 Using Division Method or Euclidean Algorithm Method</h2>
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<p>Find the GCF of 45 and 76 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>
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<p>Find the GCF of 45 and 76 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 76 by 45 76 ÷ 45 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 76 - (45 × 1) = 31</p>
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<p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 76 by 45 76 ÷ 45 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 76 - (45 × 1) = 31</p>
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<p>The remainder is 31, not zero, so continue the process</p>
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<p>The remainder is 31, not zero, so continue the process</p>
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<p><strong>Step 2:</strong>Now divide the previous divisor (45) by the previous remainder (31) 45 ÷ 31 = 1 (quotient), remainder = 45 - (31 × 1) = 14</p>
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<p><strong>Step 2:</strong>Now divide the previous divisor (45) by the previous remainder (31) 45 ÷ 31 = 1 (quotient), remainder = 45 - (31 × 1) = 14</p>
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<p><strong>Step 3:</strong>Continue the process 31 ÷ 14 = 2 (quotient), remainder = 31 - (14 × 2) = 3</p>
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<p><strong>Step 3:</strong>Continue the process 31 ÷ 14 = 2 (quotient), remainder = 31 - (14 × 2) = 3</p>
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<p><strong>Step 4:</strong>Continue the process 14 ÷ 3 = 4 (quotient), remainder = 14 - (3 × 4) = 2</p>
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<p><strong>Step 4:</strong>Continue the process 14 ÷ 3 = 4 (quotient), remainder = 14 - (3 × 4) = 2</p>
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<p><strong>Step 5:</strong>Continue the process 3 ÷ 2 = 1 (quotient), remainder = 3 - (2 × 1) = 1</p>
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<p><strong>Step 5:</strong>Continue the process 3 ÷ 2 = 1 (quotient), remainder = 3 - (2 × 1) = 1</p>
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<p><strong>Step 6:</strong>Continue the process 2 ÷ 1 = 2 (quotient), remainder = 2 - (1 × 2) = 0</p>
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<p><strong>Step 6:</strong>Continue the process 2 ÷ 1 = 2 (quotient), remainder = 2 - (1 × 2) = 0</p>
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<p>The remainder is zero, so the divisor will become the GCF. The GCF of 45 and 76 is 1.</p>
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<p>The remainder is zero, so the divisor will become the GCF. The GCF of 45 and 76 is 1.</p>
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<h2>Common Mistakes and How to Avoid Them in GCF of 45 and 76</h2>
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<h2>Common Mistakes and How to Avoid Them in GCF of 45 and 76</h2>
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<p>Finding the GCF of 45 and 76 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 45 and 76 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 teacher has 45 apples and 76 oranges. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?</p>
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<p>A teacher has 45 apples and 76 oranges. She wants to group them into equal sets, with the largest number of items in each 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>We should find the GCF of 45 and 76. The GCF of 45 and 76 is 1.</p>
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<p>We should find the GCF of 45 and 76. The GCF of 45 and 76 is 1.</p>
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<p>There will be 1 group, with each group having 45 apples and 76 oranges.</p>
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<p>There will be 1 group, with each group having 45 apples and 76 oranges.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>As the GCF of 45 and 76 is 1, the teacher can make only 1 group. Each group will consist of 45 apples and 76 oranges.</p>
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<p>As the GCF of 45 and 76 is 1, the teacher can make only 1 group. Each group will consist of 45 apples and 76 oranges.</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 45 red chairs and 76 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?</p>
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<p>A school has 45 red chairs and 76 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs 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>The GCF of 45 and 76 is 1. So each row will have 1 chair.</p>
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<p>The GCF of 45 and 76 is 1. So each row will have 1 chair.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>There are 45 red and 76 blue chairs. To find the total number of chairs in each row, we should find the GCF of 45 and 76. There will be 1 chair in each row.</p>
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<p>There are 45 red and 76 blue chairs. To find the total number of chairs in each row, we should find the GCF of 45 and 76. There will be 1 chair 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 3</h3>
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<h3>Problem 3</h3>
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<p>A tailor has 45 meters of red fabric and 76 meters of blue 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 45 meters of red fabric and 76 meters of blue 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 45 and 76.</p>
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<p>For calculating the longest equal length, we have to calculate the GCF of 45 and 76.</p>
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<p>The GCF of 45 and 76 is 1. The fabric is 1 meter long.</p>
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<p>The GCF of 45 and 76 is 1. The fabric is 1 meter 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, we first need to calculate the GCF of 45 and 76, which is 1. The length of each piece of fabric will be 1 meter.</p>
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<p>For calculating the longest length of the fabric, we first need to calculate the GCF of 45 and 76, which is 1. The length of each piece of fabric 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 45 cm long and the other 76 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 45 cm long and the other 76 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. The GCF of 45 and 76 is 1.</p>
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<p>The carpenter needs the longest piece of wood. The GCF of 45 and 76 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, 45 cm and 76 cm, respectively, we have to find the GCF of 45 and 76, which is 1 cm. The longest length of each piece is 1 cm.</p>
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<p>To find the longest length of each piece of the two wooden planks, 45 cm and 76 cm, respectively, we have to find the GCF of 45 and 76, which is 1 cm. 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 45 and ‘b’ is 15, and the LCM is 225. Find ‘b’.</p>
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<p>If the GCF of 45 and ‘b’ is 15, and the LCM is 225. 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 75.</p>
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<p>The value of ‘b’ is 75.</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>15 × 225 = 45 × b</p>
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<p>15 × 225 = 45 × b</p>
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<p>3375 = 45b</p>
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<p>3375 = 45b</p>
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<p>b = 3375 ÷ 45 = 75</p>
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<p>b = 3375 ÷ 45 = 75</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 45 and 76</h2>
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<h2>FAQs on the Greatest Common Factor of 45 and 76</h2>
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<h3>1.What is the LCM of 45 and 76?</h3>
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<h3>1.What is the LCM of 45 and 76?</h3>
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<p>The LCM of 45 and 76 is 3420.</p>
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<p>The LCM of 45 and 76 is 3420.</p>
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<h3>2.Is 45 divisible by 2?</h3>
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<h3>2.Is 45 divisible by 2?</h3>
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<p>No, 45 is not divisible by 2 because it is an odd number.</p>
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<p>No, 45 is not divisible by 2 because it is an odd 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 76?</h3>
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<h3>4.What is the prime factorization of 76?</h3>
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<p>The prime factorization of 76 is 2² × 19.</p>
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<p>The prime factorization of 76 is 2² × 19.</p>
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<h3>5.Are 45 and 76 prime numbers?</h3>
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<h3>5.Are 45 and 76 prime numbers?</h3>
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<p>No, 45 and 76 are not prime numbers because both of them have more than two factors.</p>
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<p>No, 45 and 76 are not prime numbers because both of them have more than two factors.</p>
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<h2>Important Glossaries for GCF of 45 and 76</h2>
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<h2>Important Glossaries for GCF of 45 and 76</h2>
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<ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.</li>
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<ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.</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 3 are 3, 6, 9, 12, 15, 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 3 are 3, 6, 9, 12, 15, 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 18 are 2 and 3.</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 18 are 2 and 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 9 is divided by 4, the remainder is 1 and the quotient is 2.</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 9 is divided by 4, the remainder is 1 and the quotient is 2.</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 5 and 6 is 30.</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 5 and 6 is 30.</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>