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2 <p>Last updated on<strong>August 5, 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 items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 48 and 64.</p>

4 <h2>What is the GCF of 48 and 64?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>48 and 64 is 16. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the numbers. 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>

6 <h2>How to find the GCF of 48 and 64?</h2>

7 <p>To find the GCF of 48 and 64, a few methods are described below -</p>

8 <ul><li>Listing Factors</li>

9 <li>Prime Factorization</li>

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

11 </ul><h2>GCF of 48 and 64 by Using Listing of factors</h2>

12 <p>Steps to find the GCF of 48 and 64 using the listing of<a>factors</a></p>

13 <p><strong>Step 1:</strong>Firstly, list the factors of each number</p>

14 <p>Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.</p>

15 <p>Factors of 64 = 1, 2, 4, 8, 16, 32, 64.</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 48 and 64: 1, 2, 4, 8, 16.</p>

17 <p><strong>Step 3:</strong>Choose the largest factor</p>

18 <p>The largest factor that both numbers have is 16.</p>

19 <p>The GCF of 48 and 64 is 16.</p>

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22 <h2>GCF of 48 and 64 Using Prime Factorization</h2>

21 <h2>GCF of 48 and 64 Using Prime Factorization</h2>

23 <p>To find the GCF of 48 and 64 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 48 and 64 using the Prime Factorization Method, follow these steps:</p>

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

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

25 <p>Prime Factors of 48: 48 = 2 x 2 x 2 x 2 x 3 = 2^4 x 3</p>

24 <p>Prime Factors of 48: 48 = 2 x 2 x 2 x 2 x 3 = 2^4 x 3</p>

26 <p>Prime Factors of 64: 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2^6</p>

25 <p>Prime Factors of 64: 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2^6</p>

27 <p><strong>Step 2:</strong>Now, identify the common prime factors</p>

26 <p><strong>Step 2:</strong>Now, identify the common prime factors</p>

28 <p>The common prime factors are: 2 x 2 x 2 x 2 = 2^4</p>

27 <p>The common prime factors are: 2 x 2 x 2 x 2 = 2^4</p>

29 <p><strong>Step 3:</strong>Multiply the common prime factors 2^4 = 16.</p>

28 <p><strong>Step 3:</strong>Multiply the common prime factors 2^4 = 16.</p>

30 <p>The Greatest Common Factor of 48 and 64 is 16.</p>

29 <p>The Greatest Common Factor of 48 and 64 is 16.</p>

31 <h2>GCF of 48 and 64 Using Division Method or Euclidean Algorithm Method</h2>

30 <h2>GCF of 48 and 64 Using Division Method or Euclidean Algorithm Method</h2>

32 <p>Find the GCF of 48 and 64 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

31 <p>Find the GCF of 48 and 64 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

33 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number</p>

32 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number</p>

34 <p>Here, divide 64 by 48 64 ÷ 48 = 1 (<a>quotient</a>),</p>

33 <p>Here, divide 64 by 48 64 ÷ 48 = 1 (<a>quotient</a>),</p>

35 <p>The<a>remainder</a>is calculated as 64 - (48×1) = 16</p>

34 <p>The<a>remainder</a>is calculated as 64 - (48×1) = 16</p>

36 <p>The remainder is 16, not zero, so continue the process</p>

35 <p>The remainder is 16, not zero, so continue the process</p>

37 <p><strong>Step 2:</strong>Now divide the previous divisor (48) by the previous remainder (16)</p>

36 <p><strong>Step 2:</strong>Now divide the previous divisor (48) by the previous remainder (16)</p>

38 <p>Divide 48 by 16 48 ÷ 16 = 3 (quotient), remainder = 48 - (16×3) = 0</p>

37 <p>Divide 48 by 16 48 ÷ 16 = 3 (quotient), remainder = 48 - (16×3) = 0</p>

39 <p>The remainder is zero, the divisor will become the GCF.</p>

38 <p>The remainder is zero, the divisor will become the GCF.</p>

40 <p>The GCF of 48 and 64 is 16.</p>

39 <p>The GCF of 48 and 64 is 16.</p>

41 <h2>Common Mistakes and How to Avoid Them in GCF of 48 and 64</h2>

40 <h2>Common Mistakes and How to Avoid Them in GCF of 48 and 64</h2>

42 <p>Finding GCF of 48 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>

41 <p>Finding GCF of 48 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>

43 <h3>Problem 1</h3>

42 <h3>Problem 1</h3>

44 <p>A gardener has 48 rose plants and 64 sunflower plants. She wants to group them into equal sets, with the largest number of plants in each group. How many plants will be in each group?</p>

43 <p>A gardener has 48 rose plants and 64 sunflower plants. She wants to group them into equal sets, with the largest number of plants in each group. How many plants will be in each group?</p>

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

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

46 <p>We should find the GCF of 48 and 64 GCF of 48 and 64 2^4 = 16.</p>

45 <p>We should find the GCF of 48 and 64 GCF of 48 and 64 2^4 = 16.</p>

47 <p>There are 16 equal groups 48 ÷ 16 = 3 64 ÷ 16 = 4</p>

46 <p>There are 16 equal groups 48 ÷ 16 = 3 64 ÷ 16 = 4</p>

48 <p>There will be 16 groups, and each group gets 3 rose plants and 4 sunflower plants.</p>

47 <p>There will be 16 groups, and each group gets 3 rose plants and 4 sunflower plants.</p>

49 <h3>Explanation</h3>

48 <h3>Explanation</h3>

50 <p>As the GCF of 48 and 64 is 16, the gardener can make 16 groups. Now divide 48 and 64 by 16. Each group gets 3 rose plants and 4 sunflower plants.</p>

49 <p>As the GCF of 48 and 64 is 16, the gardener can make 16 groups. Now divide 48 and 64 by 16. Each group gets 3 rose plants and 4 sunflower plants.</p>

51 <p>Well explained 👍</p>

50 <p>Well explained 👍</p>

52 <h3>Problem 2</h3>

51 <h3>Problem 2</h3>

53 <p>A bakery has 48 chocolate cupcakes and 64 vanilla cupcakes. They want to arrange them in trays with the same number of cupcakes on each tray, using the largest possible number of cupcakes per tray. How many cupcakes will be on each tray?</p>

52 <p>A bakery has 48 chocolate cupcakes and 64 vanilla cupcakes. They want to arrange them in trays with the same number of cupcakes on each tray, using the largest possible number of cupcakes per tray. How many cupcakes will be on each tray?</p>

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

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

55 <p>GCF of 48 and 64 2^4 = 16.</p>

54 <p>GCF of 48 and 64 2^4 = 16.</p>

56 <p>So each tray will have 16 cupcakes.</p>

55 <p>So each tray will have 16 cupcakes.</p>

57 <h3>Explanation</h3>

56 <h3>Explanation</h3>

58 <p>There are 48 chocolate and 64 vanilla cupcakes. To find the total number of cupcakes on each tray, we should find the GCF of 48 and 64. There will be 16 cupcakes on each tray.</p>

57 <p>There are 48 chocolate and 64 vanilla cupcakes. To find the total number of cupcakes on each tray, we should find the GCF of 48 and 64. There will be 16 cupcakes on each tray.</p>

59 <p>Well explained 👍</p>

58 <p>Well explained 👍</p>

60 <h3>Problem 3</h3>

59 <h3>Problem 3</h3>

61 <p>A ribbon factory has 48 meters of green ribbon and 64 meters of blue ribbon. They want to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

60 <p>A ribbon factory has 48 meters of green ribbon and 64 meters of blue ribbon. They want to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

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

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

63 <p>For calculating the longest equal length, we have to calculate the GCF of 48 and 64</p>

62 <p>For calculating the longest equal length, we have to calculate the GCF of 48 and 64</p>

64 <p>The GCF of 48 and 64 2^4 = 16.</p>

63 <p>The GCF of 48 and 64 2^4 = 16.</p>

65 <p>The ribbon is 16 meters long.</p>

64 <p>The ribbon is 16 meters long.</p>

66 <h3>Explanation</h3>

65 <h3>Explanation</h3>

67 <p>For calculating the longest length of the ribbon first, we need to calculate the GCF of 48 and 64, which is 16. The length of each piece of the ribbon will be 16 meters.</p>

66 <p>For calculating the longest length of the ribbon first, we need to calculate the GCF of 48 and 64, which is 16. The length of each piece of the ribbon will be 16 meters.</p>

68 <p>Well explained 👍</p>

67 <p>Well explained 👍</p>

69 <h3>Problem 4</h3>

68 <h3>Problem 4</h3>

70 <p>A carpenter has two wooden planks, one 48 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>

69 <p>A carpenter has two wooden planks, one 48 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>

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

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

72 <p>The carpenter needs the longest piece of wood GCF of 48 and 64 2^4 = 16.</p>

71 <p>The carpenter needs the longest piece of wood GCF of 48 and 64 2^4 = 16.</p>

73 <p>The longest length of each piece is 16 cm.</p>

72 <p>The longest length of each piece is 16 cm.</p>

74 <h3>Explanation</h3>

73 <h3>Explanation</h3>

75 <p>To find the longest length of each piece of the two wooden planks, 48 cm and 64 cm, respectively. We have to find the GCF of 48 and 64, which is 16 cm. The longest length of each piece is 16 cm.</p>

74 <p>To find the longest length of each piece of the two wooden planks, 48 cm and 64 cm, respectively. We have to find the GCF of 48 and 64, which is 16 cm. The longest length of each piece is 16 cm.</p>

76 <p>Well explained 👍</p>

75 <p>Well explained 👍</p>

77 <h3>Problem 5</h3>

76 <h3>Problem 5</h3>

78 <p>If the GCF of 48 and ‘b’ is 16, and the LCM is 192. Find ‘b’.</p>

77 <p>If the GCF of 48 and ‘b’ is 16, and the LCM is 192. Find ‘b’.</p>

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

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

80 <p>The value of ‘b’ is 64.</p>

79 <p>The value of ‘b’ is 64.</p>

81 <h3>Explanation</h3>

80 <h3>Explanation</h3>

82 <p>GCF x LCM = product of the numbers 16 × 192 = 48 × b</p>

81 <p>GCF x LCM = product of the numbers 16 × 192 = 48 × b</p>

83 <p>3072 = 48b</p>

82 <p>3072 = 48b</p>

84 <p>b = 3072 ÷ 48 = 64</p>

83 <p>b = 3072 ÷ 48 = 64</p>

85 <p>Well explained 👍</p>

84 <p>Well explained 👍</p>

86 <h2>FAQs on the Greatest Common Factor of 48 and 64</h2>

85 <h2>FAQs on the Greatest Common Factor of 48 and 64</h2>

87 <h3>1.What is the LCM of 48 and 64?</h3>

86 <h3>1.What is the LCM of 48 and 64?</h3>

88 <p>The LCM of 48 and 64 is 192.</p>

87 <p>The LCM of 48 and 64 is 192.</p>

89 <h3>2.Is 64 divisible by 2?</h3>

88 <h3>2.Is 64 divisible by 2?</h3>

90 <p>Yes, 64 is divisible by 2 because it is an even number.</p>

89 <p>Yes, 64 is divisible by 2 because it is an even number.</p>

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

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

92 <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>

91 <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>

93 <h3>4.What is the prime factorization of 48?</h3>

92 <h3>4.What is the prime factorization of 48?</h3>

94 <p>The prime factorization of 48 is 2^4 x 3.</p>

93 <p>The prime factorization of 48 is 2^4 x 3.</p>

95 <h3>5.Are 48 and 64 prime numbers?</h3>

94 <h3>5.Are 48 and 64 prime numbers?</h3>

96 <p>No, 48 and 64 are not prime numbers because both of them have more than two factors.</p>

95 <p>No, 48 and 64 are not prime numbers because both of them have more than two factors.</p>

97 <h2>Important Glossaries for GCF of 48 and 64</h2>

96 <h2>Important Glossaries for GCF of 48 and 64</h2>

98 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.</li>

97 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.</li>

99 <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>

98 <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>

100 <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 48 are 2 and 3.</li>

99 <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 48 are 2 and 3.</li>

101 <li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.</li>

100 <li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.</li>

102 <li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 48 and 64 is 192.</li>

101 <li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 48 and 64 is 192.</li>

103 <li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 48 and 64 is 16, as it is their largest common factor that divides the numbers completely.</li>

102 <li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 48 and 64 is 16, as it is their largest common factor that divides the numbers completely.</li>

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

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

105 <p>▶</p>

104 <p>▶</p>

106 <h2>Hiralee Lalitkumar Makwana</h2>

105 <h2>Hiralee Lalitkumar Makwana</h2>

107 <h3>About the Author</h3>

106 <h3>About the Author</h3>

108 <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>

107 <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>

109 <h3>Fun Fact</h3>

108 <h3>Fun Fact</h3>

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

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