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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 12 and 36.</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 12 and 36.</p>
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<h2>What is the GCF of 12 and 36?</h2>
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<h2>What is the GCF of 12 and 36?</h2>
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<p>The<a>greatest common factor</a>of 12 and 36 is 12. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF. 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 12 and 36 is 12. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF. 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 12 and 36?</h2>
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<h2>How to find the GCF of 12 and 36?</h2>
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<p>To find the GCF of 12 and 36, a few methods are described below -</p>
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<p>To find the GCF of 12 and 36, 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 12 and 36 by Using Listing of factors</h2>
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</ul><h2>GCF of 12 and 36 by Using Listing of factors</h2>
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<p>Steps to find the GCF of 12 and 36 using the listing of<a>factors</a></p>
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<p>Steps to find the GCF of 12 and 36 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 12 = 1, 2, 3, 4, 6, 12.</p>
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<p>Factors of 12 = 1, 2, 3, 4, 6, 12.</p>
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<p>Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.</p>
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<p>Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.</p>
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<p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 12 and 36: 1, 2, 3, 4, 6, 12.</p>
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<p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 12 and 36: 1, 2, 3, 4, 6, 12.</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 12.</p>
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<p>The largest factor that both numbers have is 12.</p>
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<p>The GCF of 12 and 36 is 12.</p>
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<p>The GCF of 12 and 36 is 12.</p>
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<h2>GCF of 12 and 36 Using Prime Factorization</h2>
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<h2>GCF of 12 and 36 Using Prime Factorization</h2>
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<p>To find the GCF of 12 and 36 using the Prime Factorization Method, follow these steps:</p>
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<p>To find the GCF of 12 and 36 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 12: 12 = 2 x 2 x 3 = 2² x 3</p>
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<p>Prime Factors of 12: 12 = 2 x 2 x 3 = 2² x 3</p>
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<p>Prime Factors of 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²</p>
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<p>Prime Factors of 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²</p>
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<p><strong>Step 2:</strong>Now, identify the common prime factors</p>
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<p><strong>Step 2:</strong>Now, identify the common prime factors</p>
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<p>The common prime factors are: 2 x 2 x 3 = 2² x 3</p>
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<p>The common prime factors are: 2 x 2 x 3 = 2² x 3</p>
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<p><strong>Step 3:</strong>Multiply the common prime factors 2² x 3 = 4 x 3 = 12.</p>
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<p><strong>Step 3:</strong>Multiply the common prime factors 2² x 3 = 4 x 3 = 12.</p>
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<p>The Greatest Common Factor of 12 and 36 is 12.</p>
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<p>The Greatest Common Factor of 12 and 36 is 12.</p>
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<h2>GCF of 12 and 36 Using Division Method or Euclidean Algorithm Method</h2>
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<h2>GCF of 12 and 36 Using Division Method or Euclidean Algorithm Method</h2>
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<p>Find the GCF of 12 and 36 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>
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<p>Find the GCF of 12 and 36 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 36 by 12 36 ÷ 12 = 3 (<a>quotient</a>),<a>remainder</a>= 36 - (12 x 3) = 0</p>
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<p>Here, divide 36 by 12 36 ÷ 12 = 3 (<a>quotient</a>),<a>remainder</a>= 36 - (12 x 3) = 0</p>
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<p>The remainder is zero, so the divisor will become the GCF.</p>
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<p>The remainder is zero, so the divisor will become the GCF.</p>
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<p>The GCF of 12 and 36 is 12.</p>
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<p>The GCF of 12 and 36 is 12.</p>
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<h2>Common Mistakes and How to Avoid Them in GCF of 12 and 36</h2>
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<h2>Common Mistakes and How to Avoid Them in GCF of 12 and 36</h2>
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<p>Finding GCF of 12 and 36 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 12 and 36 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 farmer has 12 apples and 36 oranges. He wants to pack them into equal baskets, with the largest number of items in each basket. How many items will be in each basket?</p>
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<p>A farmer has 12 apples and 36 oranges. He wants to pack them into equal baskets, with the largest number of items in each basket. How many items 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>We should find the GCF of 12 and 36 GCF of 12 and 36 2² x 3 = 4 x 3 = 12.</p>
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<p>We should find the GCF of 12 and 36 GCF of 12 and 36 2² x 3 = 4 x 3 = 12.</p>
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<p>There are 12 equal baskets. 12 ÷ 12 = 1 36 ÷ 12 = 3</p>
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<p>There are 12 equal baskets. 12 ÷ 12 = 1 36 ÷ 12 = 3</p>
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<p>There will be 12 baskets, and each basket gets 1 apple and 3 oranges.</p>
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<p>There will be 12 baskets, and each basket gets 1 apple and 3 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 12 and 36 is 12, the farmer can make 12 baskets. Now divide 12 and 36 by 12. Each basket gets 1 apple and 3 oranges.</p>
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<p>As the GCF of 12 and 36 is 12, the farmer can make 12 baskets. Now divide 12 and 36 by 12. Each basket gets 1 apple and 3 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 decorator has 12 red balloons and 36 blue balloons. They want to arrange them in rows with the same number of balloons in each row, using the largest possible number of balloons per row. How many balloons will be in each row?</p>
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<p>A decorator has 12 red balloons and 36 blue balloons. They want to arrange them in rows with the same number of balloons in each row, using the largest possible number of balloons per row. How many balloons 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>GCF of 12 and 36 2² x 3 = 4 x 3 = 12</p>
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<p>GCF of 12 and 36 2² x 3 = 4 x 3 = 12</p>
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<p>. So each row will have 12 balloons.</p>
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<p>. So each row will have 12 balloons.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>There are 12 red and 36 blue balloons. To find the total number of balloons in each row, we should find the GCF of 12 and 36. There will be 12 balloons in each row.</p>
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<p>There are 12 red and 36 blue balloons. To find the total number of balloons in each row, we should find the GCF of 12 and 36. There will be 12 balloons 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 weaver has 12 meters of cotton thread and 36 meters of wool thread. She wants to cut both threads 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 weaver has 12 meters of cotton thread and 36 meters of wool thread. She wants to cut both threads 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 12 and 36</p>
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<p>For calculating the longest equal length, we have to calculate the GCF of 12 and 36</p>
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<p>The GCF of 12 and 36</p>
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<p>The GCF of 12 and 36</p>
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<p>2² x 3 = 4 x 3 = 12.</p>
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<p>2² x 3 = 4 x 3 = 12.</p>
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<p>The thread is 12 meters long.</p>
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<p>The thread is 12 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 thread, we first need to calculate the GCF of 12 and 36, which is 12. The length of each piece of the thread will be 12 meters.</p>
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<p>For calculating the longest length of the thread, we first need to calculate the GCF of 12 and 36, which is 12. The length of each piece of the thread will be 12 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 12 cm long and the other 36 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 12 cm long and the other 36 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 12 and 36</p>
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<p>The carpenter needs the longest piece of wood GCF of 12 and 36</p>
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<p>2² x 3 = 4 x 3 = 12.</p>
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<p>2² x 3 = 4 x 3 = 12.</p>
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<p>The longest length of each piece is 12 cm.</p>
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<p>The longest length of each piece is 12 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, 12 cm and 36 cm, respectively, we have to find the GCF of 12 and 36, which is 12 cm. The longest length of each piece is 12 cm.</p>
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<p>To find the longest length of each piece of the two wooden planks, 12 cm and 36 cm, respectively, we have to find the GCF of 12 and 36, which is 12 cm. The longest length of each piece is 12 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 12 and ‘a’ is 12, and the LCM is 36. Find ‘a’.</p>
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<p>If the GCF of 12 and ‘a’ is 12, and the LCM is 36. Find ‘a’.</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 ‘a’ is 36.</p>
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<p>The value of ‘a’ is 36.</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 12 x 36 = 12 x a</p>
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<p>GCF x LCM = product of the numbers 12 x 36 = 12 x a</p>
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<p>432 = 12a</p>
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<p>432 = 12a</p>
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<p>a = 432 ÷ 12 = 36</p>
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<p>a = 432 ÷ 12 = 36</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 12 and 36</h2>
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<h2>FAQs on the Greatest Common Factor of 12 and 36</h2>
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<h3>1.What is the LCM of 12 and 36?</h3>
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<h3>1.What is the LCM of 12 and 36?</h3>
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<p>The LCM of 12 and 36 is 36.</p>
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<p>The LCM of 12 and 36 is 36.</p>
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<h3>2.Is 12 divisible by 2?</h3>
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<h3>2.Is 12 divisible by 2?</h3>
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<p>Yes, 12 is divisible by 2 because it is an even number.</p>
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<p>Yes, 12 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 36?</h3>
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<h3>4.What is the prime factorization of 36?</h3>
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<p>The prime factorization of 36 is 2² x 3².</p>
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<p>The prime factorization of 36 is 2² x 3².</p>
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<h3>5.Are 12 and 36 prime numbers?</h3>
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<h3>5.Are 12 and 36 prime numbers?</h3>
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<p>No, 12 and 36 are not prime numbers because both of them have more than two factors.</p>
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<p>No, 12 and 36 are not prime numbers because both of them have more than two factors.</p>
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<h2>Important Glossaries for GCF of 12 and 36</h2>
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<h2>Important Glossaries for GCF of 12 and 36</h2>
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<ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.</li>
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<ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.</li>
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<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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<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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<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 12 are 2 and 3.</li>
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<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 12 are 2 and 3.</li>
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<li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 5, the remainder is 4 and the quotient is 2.</li>
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<li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 5, the remainder is 4 and the quotient is 2.</li>
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<li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 12 and 36 is 36.</li>
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<li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 12 and 36 is 36.</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>