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2 <p>Last updated on<strong>August 14, 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 to schedule events. In this topic, we will learn about the GCF of 52 and 64.</p>

4 <h2>What is the GCF of 52 and 64?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>52 and 64 is 4. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the numbers.</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 52 and 64?</h2>

8 <p>To find the GCF of 52 and 64, 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 52 and 64 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 52 and 64 using the listing of<a>factors</a></p>

14 <p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 52 = 1, 2, 4, 13, 26, 52. Factors of 64 = 1, 2, 4, 8, 16, 32, 64.</p>

15 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 52 and 64: 1, 2, 4.</p>

16 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 4. The GCF of 52 and 64 is 4.</p>

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19 <h2>GCF of 52 and 64 Using Prime Factorization</h2>

18 <h2>GCF of 52 and 64 Using Prime Factorization</h2>

20 <p>To find the GCF of 52 and 64 using the Prime Factorization Method, follow these steps:</p>

19 <p>To find the GCF of 52 and 64 using the Prime Factorization Method, follow these steps:</p>

21 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number</p>

20 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number</p>

22 <p>Prime Factors of 52: 52 = 2 × 2 × 13 = 2² × 13</p>

21 <p>Prime Factors of 52: 52 = 2 × 2 × 13 = 2² × 13</p>

23 <p>Prime Factors of 64: 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶</p>

22 <p>Prime Factors of 64: 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶</p>

24 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 2 × 2 = 2²</p>

23 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 2 × 2 = 2²</p>

25 <p><strong>Step 3:</strong>Multiply the common prime factors 2² = 4. The Greatest Common Factor of 52 and 64 is 4.</p>

24 <p><strong>Step 3:</strong>Multiply the common prime factors 2² = 4. The Greatest Common Factor of 52 and 64 is 4.</p>

26 <h2>GCF of 52 and 64 Using Division Method or Euclidean Algorithm Method</h2>

25 <h2>GCF of 52 and 64 Using Division Method or Euclidean Algorithm Method</h2>

27 <p>Find the GCF of 52 and 64 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

26 <p>Find the GCF of 52 and 64 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

28 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 64 by 52 64 ÷ 52 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 64 - (52×1) = 12</p>

27 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 64 by 52 64 ÷ 52 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 64 - (52×1) = 12</p>

29 <p>The remainder is 12, not zero, so continue the process</p>

28 <p>The remainder is 12, not zero, so continue the process</p>

30 <p><strong>Step 2:</strong>Now divide the previous divisor (52) by the previous remainder (12) Divide 52 by 12 52 ÷ 12 = 4 (quotient), remainder = 52 - (12×4) = 4</p>

29 <p><strong>Step 2:</strong>Now divide the previous divisor (52) by the previous remainder (12) Divide 52 by 12 52 ÷ 12 = 4 (quotient), remainder = 52 - (12×4) = 4</p>

31 <p><strong>Step 3:</strong>Now divide the previous divisor (12) by the previous remainder (4) Divide 12 by 4 12 ÷ 4 = 3 (quotient), remainder = 12 - (4×3) = 0</p>

30 <p><strong>Step 3:</strong>Now divide the previous divisor (12) by the previous remainder (4) Divide 12 by 4 12 ÷ 4 = 3 (quotient), remainder = 12 - (4×3) = 0</p>

32 <p>The remainder is zero, the divisor will become the GCF. The GCF of 52 and 64 is 4.</p>

31 <p>The remainder is zero, the divisor will become the GCF. The GCF of 52 and 64 is 4.</p>

33 <h2>Common Mistakes and How to Avoid Them in GCF of 52 and 64</h2>

32 <h2>Common Mistakes and How to Avoid Them in GCF of 52 and 64</h2>

34 <p>Finding the GCF of 52 and 64 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 the GCF of 52 and 64 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 52 roses and 64 tulips. She wants to group them into equal sets, with the largest number of flowers in each group. How many flowers will be in each group?</p>

35 <p>A gardener has 52 roses and 64 tulips. She wants to group them into equal sets, with the largest number of flowers in each group. How many flowers will be in each group?</p>

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

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

38 <p>We should find the GCF of 52 and 64 GCF of 52 and 64 2² = 4.</p>

37 <p>We should find the GCF of 52 and 64 GCF of 52 and 64 2² = 4.</p>

39 <p>There are 4 equal groups 52 ÷ 4 = 13 64 ÷ 4 = 16</p>

38 <p>There are 4 equal groups 52 ÷ 4 = 13 64 ÷ 4 = 16</p>

40 <p>There will be 4 groups, and each group gets 13 roses and 16 tulips.</p>

39 <p>There will be 4 groups, and each group gets 13 roses and 16 tulips.</p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>As the GCF of 52 and 64 is 4, the gardener can make 4 groups. Now divide 52 and 64 by 4. Each group gets 13 roses and 16 tulips.</p>

41 <p>As the GCF of 52 and 64 is 4, the gardener can make 4 groups. Now divide 52 and 64 by 4. Each group gets 13 roses and 16 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 52 markers and 64 crayons. 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 52 markers and 64 crayons. 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 52 and 64 2² = 4. So each row will have 4 items.</p>

46 <p>GCF of 52 and 64 2² = 4. So each row will have 4 items.</p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>There are 52 markers and 64 crayons. To find the total number of items in each row, we should find the GCF of 52 and 64. There will be 4 items in each row.</p>

48 <p>There are 52 markers and 64 crayons. To find the total number of items in each row, we should find the GCF of 52 and 64. There will be 4 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 52 meters of silk ribbon and 64 meters of cotton ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

51 <p>A tailor has 52 meters of silk ribbon and 64 meters of cotton ribbon. She wants to cut both ribbons 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 52 and 64 The GCF of 52 and 64 2² = 4. The ribbon is 4 meters long.</p>

53 <p>For calculating the longest equal length, we have to calculate the GCF of 52 and 64 The GCF of 52 and 64 2² = 4. The ribbon is 4 meters long.</p>

55 <h3>Explanation</h3>

54 <h3>Explanation</h3>

56 <p>For calculating the longest length of the ribbon first we need to calculate the GCF of 52 and 64 which is 4. The length of each piece of the ribbon will be 4 meters.</p>

55 <p>For calculating the longest length of the ribbon first we need to calculate the GCF of 52 and 64 which is 4. The length of each piece of the ribbon will be 4 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 52 cm long and the other 64 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 52 cm long and the other 64 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 52 and 64 2² = 4. The longest length of each piece is 4 cm.</p>

60 <p>The carpenter needs the longest piece of wood GCF of 52 and 64 2² = 4. The longest length of each piece is 4 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, 52 cm and 64 cm, respectively. We have to find the GCF of 52 and 64, which is 4 cm. The longest length of each piece is 4 cm.</p>

62 <p>To find the longest length of each piece of the two wooden planks, 52 cm and 64 cm, respectively. We have to find the GCF of 52 and 64, which is 4 cm. The longest length of each piece is 4 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 52 and ‘b’ is 4, and the LCM is 832. Find ‘b’.</p>

65 <p>If the GCF of 52 and ‘b’ is 4, and the LCM is 832. Find ‘b’.</p>

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

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

68 <p>The value of ‘b’ is 64.</p>

67 <p>The value of ‘b’ is 64.</p>

69 <h3>Explanation</h3>

68 <h3>Explanation</h3>

70 <p>GCF × LCM = product of the numbers</p>

69 <p>GCF × LCM = product of the numbers</p>

71 <p>4 × 832 = 52 × b</p>

70 <p>4 × 832 = 52 × b</p>

72 <p>3328 = 52b</p>

71 <p>3328 = 52b</p>

73 <p>b = 3328 ÷ 52 = 64</p>

72 <p>b = 3328 ÷ 52 = 64</p>

74 <p>Well explained 👍</p>

73 <p>Well explained 👍</p>

75 <h2>FAQs on the Greatest Common Factor of 52 and 64</h2>

74 <h2>FAQs on the Greatest Common Factor of 52 and 64</h2>

76 <h3>1.What is the LCM of 52 and 64?</h3>

75 <h3>1.What is the LCM of 52 and 64?</h3>

77 <p>The LCM of 52 and 64 is 832.</p>

76 <p>The LCM of 52 and 64 is 832.</p>

78 <h3>2.Is 52 divisible by 2?</h3>

77 <h3>2.Is 52 divisible by 2?</h3>

79 <p>Yes, 52 is divisible by 2 because it is an even number.</p>

78 <p>Yes, 52 is divisible by 2 because it is an even number.</p>

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

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

81 <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>

80 <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>

82 <h3>4.What is the prime factorization of 64?</h3>

81 <h3>4.What is the prime factorization of 64?</h3>

83 <p>The prime factorization of 64 is 2⁶.</p>

82 <p>The prime factorization of 64 is 2⁶.</p>

84 <h3>5.Are 52 and 64 prime numbers?</h3>

83 <h3>5.Are 52 and 64 prime numbers?</h3>

85 <p>No, 52 and 64 are not prime numbers because both of them have more than two factors.</p>

84 <p>No, 52 and 64 are not prime numbers because both of them have more than two factors.</p>

86 <h2>Important Glossaries for GCF of 52 and 64</h2>

85 <h2>Important Glossaries for GCF of 52 and 64</h2>

87 <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>

86 <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>

88 </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>

87 </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>

89 </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 15 are 3 and 5.</li>

88 </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 15 are 3 and 5.</li>

90 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.</li>

89 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.</li>

91 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 52 and 64 is 832.</li>

90 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 52 and 64 is 832.</li>

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

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

93 <p>▶</p>

92 <p>▶</p>

94 <h2>Hiralee Lalitkumar Makwana</h2>

93 <h2>Hiralee Lalitkumar Makwana</h2>

95 <h3>About the Author</h3>

94 <h3>About the Author</h3>

96 <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>

95 <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>

97 <h3>Fun Fact</h3>

96 <h3>Fun Fact</h3>

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

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