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2026-01-01
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<p>Last updated on<strong>September 10, 2025</strong></p>
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<p>Last updated on<strong>September 10, 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 72 and 24.</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 72 and 24.</p>
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<h2>What is the GCF of 72 and 24?</h2>
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<h2>What is the GCF of 72 and 24?</h2>
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<p>The<a>greatest common factor</a>of 72 and 24 is 24. 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 72 and 24 is 24. 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 72 and 24?</h2>
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<h2>How to find the GCF of 72 and 24?</h2>
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<p>To find the GCF of 72 and 24, a few methods are described below -</p>
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<p>To find the GCF of 72 and 24, 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 72 and 24 by Using Listing of factors</h2>
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</ol><h2>GCF of 72 and 24 by Using Listing of factors</h2>
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<p>Steps to find the GCF of 72 and 24 using the listing of<a>factors</a>:</p>
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<p>Steps to find the GCF of 72 and 24 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 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.</p>
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<p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.</p>
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<p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 72 and 24: 1, 2, 3, 4, 6, 8, 12, 24.</p>
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<p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 72 and 24: 1, 2, 3, 4, 6, 8, 12, 24.</p>
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<p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 24. The GCF of 72 and 24 is 24.</p>
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<p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 24. The GCF of 72 and 24 is 24.</p>
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<h2>GCF of 72 and 24 Using Prime Factorization</h2>
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<h2>GCF of 72 and 24 Using Prime Factorization</h2>
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<p>To find the GCF of 72 and 24 using the Prime Factorization Method, follow these steps:</p>
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<p>To find the GCF of 72 and 24 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 72: 72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²</p>
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<p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 72: 72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²</p>
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<p>Prime Factors of 24: 24 = 2 x 2 x 2 x 3 = 2³ x 3</p>
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<p>Prime Factors of 24: 24 = 2 x 2 x 2 x 3 = 2³ x 3</p>
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<p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2³ x 3</p>
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<p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2³ x 3</p>
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<p><strong>Step 3:</strong>Multiply the common prime factors 2³ x 3 = 8 x 3 = 24. The Greatest Common Factor of 72 and 24 is 24.</p>
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<p><strong>Step 3:</strong>Multiply the common prime factors 2³ x 3 = 8 x 3 = 24. The Greatest Common Factor of 72 and 24 is 24.</p>
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<h2>GCF of 72 and 24 Using Division Method or Euclidean Algorithm Method</h2>
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<h2>GCF of 72 and 24 Using Division Method or Euclidean Algorithm Method</h2>
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<p>Find the GCF of 72 and 24 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>
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<p>Find the GCF of 72 and 24 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 72 by 24 72 ÷ 24 = 3 (<a>quotient</a>),<a>remainder</a>= 72 - (24×3) = 0</p>
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<p>Here, divide 72 by 24 72 ÷ 24 = 3 (<a>quotient</a>),<a>remainder</a>= 72 - (24×3) = 0</p>
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<p>The remainder is zero, the divisor will become the GCF. The GCF of 72 and 24 is 24.</p>
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<p>The remainder is zero, the divisor will become the GCF. The GCF of 72 and 24 is 24.</p>
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<h2>Common Mistakes and How to Avoid Them in GCF of 72 and 24</h2>
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<h2>Common Mistakes and How to Avoid Them in GCF of 72 and 24</h2>
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<p>Finding GCF of 72 and 24 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 72 and 24 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>A baker has 72 cookies and 24 cupcakes. She wants to pack them into boxes with the largest number of items in each box. How many items will be in each box?</p>
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<p>A baker has 72 cookies and 24 cupcakes. She wants to pack them into boxes with the largest number of items in each box. How many items will be in each box?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>We should find the GCF of 72 and 24 GCF of 72 and 24 2³ x 3 = 8 x 3 = 24.</p>
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<p>We should find the GCF of 72 and 24 GCF of 72 and 24 2³ x 3 = 8 x 3 = 24.</p>
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<p>There are 24 equal boxes 72 ÷ 24 = 3 24 ÷ 24 = 1</p>
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<p>There are 24 equal boxes 72 ÷ 24 = 3 24 ÷ 24 = 1</p>
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<p>There will be 24 boxes, and each box gets 3 cookies and 1 cupcake.</p>
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<p>There will be 24 boxes, and each box gets 3 cookies and 1 cupcake.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>As the GCF of 72 and 24 is 24, the baker can make 24 boxes. Now divide 72 and 24 by 24. Each box gets 3 cookies and 1 cupcake.</p>
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<p>As the GCF of 72 and 24 is 24, the baker can make 24 boxes. Now divide 72 and 24 by 24. Each box gets 3 cookies and 1 cupcake.</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 gardener has 72 red roses and 24 white roses. They want to arrange them in rows with the same number of roses in each row, using the largest possible number of roses per row. How many roses will be in each row?</p>
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<p>A gardener has 72 red roses and 24 white roses. They want to arrange them in rows with the same number of roses in each row, using the largest possible number of roses per row. How many roses 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 72 and 24 2³ x 3 = 8 x 3 = 24. So each row will have 24 roses.</p>
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<p>GCF of 72 and 24 2³ x 3 = 8 x 3 = 24. So each row will have 24 roses.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>There are 72 red roses and 24 white roses. To find the total number of roses in each row, we should find the GCF of 72 and 24. There will be 24 roses in each row.</p>
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<p>There are 72 red roses and 24 white roses. To find the total number of roses in each row, we should find the GCF of 72 and 24. There will be 24 roses 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 72 meters of red fabric and 24 meters of white 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 72 meters of red fabric and 24 meters of white 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 72 and 24</p>
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<p>For calculating the longest equal length, we have to calculate the GCF of 72 and 24</p>
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<p>The GCF of 72 and 24 2³ x 3 = 8 x 3 = 24. The fabric is 24 meters long.</p>
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<p>The GCF of 72 and 24 2³ x 3 = 8 x 3 = 24. The fabric is 24 meters long.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>For calculating the longest length of the fabric first we need to calculate the GCF of 72 and 24 which is 24. The length of each piece of the fabric will be 24 meters.</p>
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<p>For calculating the longest length of the fabric first we need to calculate the GCF of 72 and 24 which is 24. The length of each piece of the fabric will be 24 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 72 cm long and the other 24 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 72 cm long and the other 24 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 72 and 24 2³ x 3 = 8 x 3 = 24. The longest length of each piece is 24 cm.</p>
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<p>The carpenter needs the longest piece of wood GCF of 72 and 24 2³ x 3 = 8 x 3 = 24. The longest length of each piece is 24 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, 72 cm and 24 cm, respectively. We have to find the GCF of 72 and 24, which is 24 cm. The longest length of each piece is 24 cm.</p>
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<p>To find the longest length of each piece of the two wooden planks, 72 cm and 24 cm, respectively. We have to find the GCF of 72 and 24, which is 24 cm. The longest length of each piece is 24 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 72 and ‘a’ is 24, and the LCM is 144. Find ‘a’.</p>
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<p>If the GCF of 72 and ‘a’ is 24, and the LCM is 144. 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 48.</p>
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<p>The value of ‘a’ is 48.</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>24 × 144 = 72 × a</p>
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<p>24 × 144 = 72 × a</p>
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<p>3456 = 72a</p>
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<p>3456 = 72a</p>
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<p>a = 3456 ÷ 72 = 48</p>
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<p>a = 3456 ÷ 72 = 48</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 72 and 24</h2>
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<h2>FAQs on the Greatest Common Factor of 72 and 24</h2>
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<h3>1.What is the LCM of 72 and 24?</h3>
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<h3>1.What is the LCM of 72 and 24?</h3>
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<p>The LCM of 72 and 24 is 72.</p>
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<p>The LCM of 72 and 24 is 72.</p>
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<h3>2.Is 72 divisible by 8?</h3>
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<h3>2.Is 72 divisible by 8?</h3>
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<p>Yes, 72 is divisible by 8 because 72 divided by 8 equals 9.</p>
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<p>Yes, 72 is divisible by 8 because 72 divided by 8 equals 9.</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 24?</h3>
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<h3>4.What is the prime factorization of 24?</h3>
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<p>The prime factorization of 24 is 2³ x 3.</p>
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<p>The prime factorization of 24 is 2³ x 3.</p>
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<h3>5.Are 72 and 24 prime numbers?</h3>
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<h3>5.Are 72 and 24 prime numbers?</h3>
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<p>No, 72 and 24 are not prime numbers because both of them have more than two factors.</p>
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<p>No, 72 and 24 are not prime numbers because both of them have more than two factors.</p>
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<h2>Important Glossaries for GCF of 72 and 24</h2>
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<h2>Important Glossaries for GCF of 72 and 24</h2>
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<ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.</li>
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<ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.</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 6 are 6, 12, 18, 24, 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 6 are 6, 12, 18, 24, 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 15 is divided by 4, the remainder is 3, 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 15 is divided by 4, the remainder is 3, 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 72 and 24 is 72.</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 72 and 24 is 72.</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>