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2 <p>Last updated on<strong>August 11, 2025</strong></p>

3 <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 24 and 32.</p>

4 <h2>What is the GCF of 24 and 32?</h2>

5 <p>The<a>greatest common factor</a>of 24 and 32 is 8. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number.</p>

6 <p>If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.</p>

7 <h2>How to find the GCF of 24 and 32?</h2>

8 <p>To find the GCF of 24 and 32, a few methods are described below -</p>

9 <ol><li>Listing Factors</li>

10 <li>Prime Factorization</li>

11 <li>Long Division Method / by Euclidean Algorithm</li>

12 </ol><h2>GCF of 24 and 32 by Using Listing of factors</h2>

13 <p>Steps to find the GCF of 24 and 32 using the listing of<a>factors</a></p>

14 <p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.</p>

15 <p>Factors of 32 = 1, 2, 4, 8, 16, 32.</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 24 and 32: 1, 2, 4, 8.</p>

17 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 8. The GCF of 24 and 32 is 8.</p>

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20 <h2>GCF of 24 and 32 Using Prime Factorization</h2>

19 <h2>GCF of 24 and 32 Using Prime Factorization</h2>

21 <p>To find the GCF of 24 and 32 using Prime Factorization Method, follow these steps:</p>

20 <p>To find the GCF of 24 and 32 using Prime Factorization Method, follow these steps:</p>

22 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 24: 24 = 2 x 2 x 2 x 3 = 23 x 3</p>

21 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 24: 24 = 2 x 2 x 2 x 3 = 23 x 3</p>

23 <p>Prime Factors of 32: 32 = 2 x 2 x 2 x 2 x 2 = 25</p>

22 <p>Prime Factors of 32: 32 = 2 x 2 x 2 x 2 x 2 = 25</p>

24 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 x 2 x 2 = 23</p>

23 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 2 x 2 x 2 = 23</p>

25 <p><strong>Step 3:</strong>Multiply the common prime factors 23 = 8.</p>

24 <p><strong>Step 3:</strong>Multiply the common prime factors 23 = 8.</p>

26 <p>The Greatest Common Factor of 24 and 32 is 8.</p>

25 <p>The Greatest Common Factor of 24 and 32 is 8.</p>

27 <h2>GCF of 24 and 32 Using Division Method or Euclidean Algorithm Method</h2>

26 <h2>GCF of 24 and 32 Using Division Method or Euclidean Algorithm Method</h2>

28 <p>Find the GCF of 24 and 32 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

27 <p>Find the GCF of 24 and 32 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

29 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 32 by 24 32 ÷ 24 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 32 - (24×1) = 8</p>

28 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 32 by 24 32 ÷ 24 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 32 - (24×1) = 8</p>

30 <p>The remainder is 8, not zero, so continue the process</p>

29 <p>The remainder is 8, not zero, so continue the process</p>

31 <p><strong>Step 2:</strong>Now divide the previous divisor (24) by the previous remainder (8) Divide 24 by 8 24 ÷ 8 = 3 (quotient), remainder = 24 - (8×3) = 0</p>

30 <p><strong>Step 2:</strong>Now divide the previous divisor (24) by the previous remainder (8) Divide 24 by 8 24 ÷ 8 = 3 (quotient), remainder = 24 - (8×3) = 0</p>

32 <p>The remainder is zero, the divisor will become the GCF. The GCF of 24 and 32 is 8.</p>

31 <p>The remainder is zero, the divisor will become the GCF. The GCF of 24 and 32 is 8.</p>

33 <h2>Common Mistakes and How to Avoid Them in GCF of 24 and 32</h2>

32 <h2>Common Mistakes and How to Avoid Them in GCF of 24 and 32</h2>

34 <p>Finding GCF of 24 and 32 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

33 <p>Finding GCF of 24 and 32 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

35 <h3>Problem 1</h3>

34 <h3>Problem 1</h3>

36 <p>A gardener has 24 roses and 32 tulips. She wants to arrange them in bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?</p>

35 <p>A gardener has 24 roses and 32 tulips. She wants to arrange them in bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?</p>

37 <p>Okay, lets begin</p>

36 <p>Okay, lets begin</p>

38 <p>We should find the GCF of 24 and 32 GCF of 24 and 32 , 23 = 8.</p>

37 <p>We should find the GCF of 24 and 32 GCF of 24 and 32 , 23 = 8.</p>

39 <p>There are 8 equal bouquets 24 ÷ 8 = 3 32 ÷ 8 = 4</p>

38 <p>There are 8 equal bouquets 24 ÷ 8 = 3 32 ÷ 8 = 4</p>

40 <p>There will be 8 bouquets, and each bouquet gets 3 roses and 4 tulips.</p>

39 <p>There will be 8 bouquets, and each bouquet gets 3 roses and 4 tulips.</p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>As the GCF of 24 and 32 is 8, the gardener can make 8 bouquets. Now divide 24 and 32 by 8. Each bouquet gets 3 roses and 4 tulips.</p>

41 <p>As the GCF of 24 and 32 is 8, the gardener can make 8 bouquets. Now divide 24 and 32 by 8. Each bouquet gets 3 roses and 4 tulips.</p>

43 <p>Well explained 👍</p>

42 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

43 <h3>Problem 2</h3>

45 <p>A school has 24 desks and 32 chairs. They want to arrange them in rows with the same number of items in each row, using the largest possible number of items per row. How many items will be in each row?</p>

44 <p>A school has 24 desks and 32 chairs. They want to arrange them in rows with the same number of items in each row, using the largest possible number of items per row. How many items will be in each row?</p>

46 <p>Okay, lets begin</p>

45 <p>Okay, lets begin</p>

47 <p>GCF of 24 and 32 23 = 8. So each row will have 8 items.</p>

46 <p>GCF of 24 and 32 23 = 8. So each row will have 8 items.</p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>There are 24 desks and 32 chairs. To find the total number of items in each row, we should find the GCF of 24 and 32. There will be 8 items in each row.</p>

48 <p>There are 24 desks and 32 chairs. To find the total number of items in each row, we should find the GCF of 24 and 32. There will be 8 items in each row.</p>

50 <p>Well explained 👍</p>

49 <p>Well explained 👍</p>

51 <h3>Problem 3</h3>

50 <h3>Problem 3</h3>

52 <p>A tailor has 24 meters of red fabric and 32 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>

51 <p>A tailor has 24 meters of red fabric and 32 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>

53 <p>Okay, lets begin</p>

52 <p>Okay, lets begin</p>

54 <p>For calculating the longest equal length, we have to calculate the GCF of 24 and 32 The GCF of 24 and 32 2^3 = 8. The fabric is 8 meters long.</p>

53 <p>For calculating the longest equal length, we have to calculate the GCF of 24 and 32 The GCF of 24 and 32 2^3 = 8. The fabric is 8 meters long.</p>

55 <h3>Explanation</h3>

54 <h3>Explanation</h3>

56 <p>For calculating the longest length of the fabric first we need to calculate the GCF of 24 and 32, which is 8. The length of each piece of the fabric will be 8 meters.</p>

55 <p>For calculating the longest length of the fabric first we need to calculate the GCF of 24 and 32, which is 8. The length of each piece of the fabric will be 8 meters.</p>

57 <p>Well explained 👍</p>

56 <p>Well explained 👍</p>

58 <h3>Problem 4</h3>

57 <h3>Problem 4</h3>

59 <p>A carpenter has two wooden planks, one 24 cm long and the other 32 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>

58 <p>A carpenter has two wooden planks, one 24 cm long and the other 32 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>

60 <p>Okay, lets begin</p>

59 <p>Okay, lets begin</p>

61 <p>The carpenter needs the longest piece of wood GCF of 24 and 32 2^3 = 8. The longest length of each piece is 8 cm.</p>

60 <p>The carpenter needs the longest piece of wood GCF of 24 and 32 2^3 = 8. The longest length of each piece is 8 cm.</p>

62 <h3>Explanation</h3>

61 <h3>Explanation</h3>

63 <p>To find the longest length of each piece of the two wooden planks, 24 cm and 32 cm, respectively. We have to find the GCF of 24 and 32, which is 8 cm. The longest length of each piece is 8 cm.</p>

62 <p>To find the longest length of each piece of the two wooden planks, 24 cm and 32 cm, respectively. We have to find the GCF of 24 and 32, which is 8 cm. The longest length of each piece is 8 cm.</p>

64 <p>Well explained 👍</p>

63 <p>Well explained 👍</p>

65 <h3>Problem 5</h3>

64 <h3>Problem 5</h3>

66 <p>If the GCF of 24 and ‘a’ is 8, and the LCM is 96. Find ‘a’.</p>

65 <p>If the GCF of 24 and ‘a’ is 8, and the LCM is 96. Find ‘a’.</p>

67 <p>Okay, lets begin</p>

66 <p>Okay, lets begin</p>

68 <p>The value of ‘a’ is 32.</p>

67 <p>The value of ‘a’ is 32.</p>

69 <h3>Explanation</h3>

68 <h3>Explanation</h3>

70 <p>GCF x LCM = product of the numbers 8 × 96 = 24 × a 768 = 24a a = 768 ÷ 24 = 32</p>

69 <p>GCF x LCM = product of the numbers 8 × 96 = 24 × a 768 = 24a a = 768 ÷ 24 = 32</p>

71 <p>Well explained 👍</p>

70 <p>Well explained 👍</p>

72 <h2>FAQs on the Greatest Common Factor of 24 and 32</h2>

71 <h2>FAQs on the Greatest Common Factor of 24 and 32</h2>

73 <h3>1.What is the LCM of 24 and 32?</h3>

72 <h3>1.What is the LCM of 24 and 32?</h3>

74 <p>The LCM of 24 and 32 is 96.</p>

73 <p>The LCM of 24 and 32 is 96.</p>

75 <h3>2.Is 24 divisible by 8?</h3>

74 <h3>2.Is 24 divisible by 8?</h3>

76 <p>Yes, 24 is divisible by 8 because 24 ÷ 8 equals 3 with no remainder.</p>

75 <p>Yes, 24 is divisible by 8 because 24 ÷ 8 equals 3 with no remainder.</p>

77 <h3>3.What will be the GCF of any two consecutive numbers?</h3>

76 <h3>3.What will be the GCF of any two consecutive numbers?</h3>

78 <p>The GCF of any two<a>consecutive numbers</a>is always 1 because consecutive numbers have no common factors other than 1.</p>

77 <p>The GCF of any two<a>consecutive numbers</a>is always 1 because consecutive numbers have no common factors other than 1.</p>

79 <h3>4.What is the prime factorization of 32?</h3>

78 <h3>4.What is the prime factorization of 32?</h3>

80 <p>The prime factorization of 32 is 25.</p>

79 <p>The prime factorization of 32 is 25.</p>

81 <h3>5.Are 24 and 32 prime numbers?</h3>

80 <h3>5.Are 24 and 32 prime numbers?</h3>

82 <p>No, 24 and 32 are not<a>prime numbers</a>because both of them have more than two factors.</p>

81 <p>No, 24 and 32 are not<a>prime numbers</a>because both of them have more than two factors.</p>

83 <h2>Important Glossaries for GCF of 24 and 32</h2>

82 <h2>Important Glossaries for GCF of 24 and 32</h2>

84 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.</li>

83 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.</li>

85 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, and so on.</li>

84 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, and so on.</li>

86 </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 10 are 2 and 5.</li>

85 </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 10 are 2 and 5.</li>

87 </ul><ul><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>

86 </ul><ul><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>

88 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 24 and 32 is 96.</li>

87 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 24 and 32 is 96.</li>

89 </ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>

88 </ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>

90 <p>▶</p>

89 <p>▶</p>

91 <h2>Hiralee Lalitkumar Makwana</h2>

90 <h2>Hiralee Lalitkumar Makwana</h2>

92 <h3>About the Author</h3>

91 <h3>About the Author</h3>

93 <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>

92 <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>

94 <h3>Fun Fact</h3>

93 <h3>Fun Fact</h3>

95 <p>: She loves to read number jokes and games.</p>

94 <p>: She loves to read number jokes and games.</p>