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2 <p>Last updated on<strong>September 20, 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 15 and 65.</p>

4 <h2>What is the GCF of 15 and 65?</h2>

5 <p>The<a>greatest common factor</a>of 15 and 65 is 5. 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.</p>

6 <p>The GCF of two numbers cannot be negative because divisors are always positive.</p>

7 <h2>How to find the GCF of 15 and 65?</h2>

8 <p>To find the GCF of 15 and 65, a few methods are described below </p>

9 <ul><li>Listing Factors </li>

10 <li>Prime Factorization </li>

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

12 </ul><h2>GCF of 15 and 65 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 15 and 65 using the listing of<a>factors</a></p>

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

15 <p>Factors of 15 = 1, 3, 5, 15.</p>

16 <p>Factors of 65 = 1, 5, 13, 65.</p>

17 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 15 and 65: 1, 5.</p>

18 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 5.</p>

19 <p>The GCF of 15 and 65 is 5.</p>

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22 <h2>GCF of 15 and 65 Using Prime Factorization</h2>

21 <h2>GCF of 15 and 65 Using Prime Factorization</h2>

23 <p>To find the GCF of 15 and 65 using Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 15 and 65 using 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 15: 15 = 3 x 5</p>

24 <p>Prime Factors of 15: 15 = 3 x 5</p>

26 <p>Prime Factors of 65: 65 = 5 x 13</p>

25 <p>Prime Factors of 65: 65 = 5 x 13</p>

27 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 5</p>

26 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 5</p>

28 <p><strong>Step 3:</strong>Multiply the common prime factors 5 = 5</p>

27 <p><strong>Step 3:</strong>Multiply the common prime factors 5 = 5</p>

29 <p>The Greatest Common Factor of 15 and 65 is 5.</p>

28 <p>The Greatest Common Factor of 15 and 65 is 5.</p>

30 <h2>GCF of 15 and 65 Using Division Method or Euclidean Algorithm Method</h2>

29 <h2>GCF of 15 and 65 Using Division Method or Euclidean Algorithm Method</h2>

31 <p>Find the GCF of 15 and 65 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

30 <p>Find the GCF of 15 and 65 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

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

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

33 <p>Here, divide 65 by 15 65 ÷ 15 = 4 (<a>quotient</a>),</p>

32 <p>Here, divide 65 by 15 65 ÷ 15 = 4 (<a>quotient</a>),</p>

34 <p>The<a>remainder</a>is calculated as 65 - (15×4) = 5</p>

33 <p>The<a>remainder</a>is calculated as 65 - (15×4) = 5</p>

35 <p>The remainder is 5, not zero, so continue the process</p>

34 <p>The remainder is 5, not zero, so continue the process</p>

36 <p><strong>Step 2:</strong>Now divide the previous divisor (15) by the previous remainder (5)</p>

35 <p><strong>Step 2:</strong>Now divide the previous divisor (15) by the previous remainder (5)</p>

37 <p>Divide 15 by 5 15 ÷ 5 = 3 (quotient), remainder = 15 - (5×3) = 0</p>

36 <p>Divide 15 by 5 15 ÷ 5 = 3 (quotient), remainder = 15 - (5×3) = 0</p>

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

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

39 <p>The GCF of 15 and 65 is 5.</p>

38 <p>The GCF of 15 and 65 is 5.</p>

40 <h2>Common Mistakes and How to Avoid Them in GCF of 15 and 65</h2>

39 <h2>Common Mistakes and How to Avoid Them in GCF of 15 and 65</h2>

41 <p>Finding the GCF of 15 and 65 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

40 <p>Finding the GCF of 15 and 65 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

42 <h3>Problem 1</h3>

41 <h3>Problem 1</h3>

43 <p>A gardener has 15 rose bushes and 65 tulip plants. He wants to plant them in equal groups, with the largest number of plants in each group. How many plants will be in each group?</p>

42 <p>A gardener has 15 rose bushes and 65 tulip plants. He wants to plant them in equal groups, with the largest number of plants in each group. How many plants will be in each group?</p>

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

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

45 <p>We should find GCF of 15 and 65 GCF of 15 and 65 5</p>

44 <p>We should find GCF of 15 and 65 GCF of 15 and 65 5</p>

46 <p>There are 5 equal groups 15 ÷ 5 = 3 65 ÷ 5 = 13</p>

45 <p>There are 5 equal groups 15 ÷ 5 = 3 65 ÷ 5 = 13</p>

47 <p>There will be 5 groups, and each group gets 3 rose bushes and 13 tulip plants.</p>

46 <p>There will be 5 groups, and each group gets 3 rose bushes and 13 tulip plants.</p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>As the GCF of 15 and 65 is 5, the gardener can make 5 groups.</p>

48 <p>As the GCF of 15 and 65 is 5, the gardener can make 5 groups.</p>

50 <p>Now divide 15 and 65 by 5.</p>

49 <p>Now divide 15 and 65 by 5.</p>

51 <p>Each group gets 3 rose bushes and 13 tulip plants.</p>

50 <p>Each group gets 3 rose bushes and 13 tulip plants.</p>

52 <p>Well explained 👍</p>

51 <p>Well explained 👍</p>

53 <h3>Problem 2</h3>

52 <h3>Problem 2</h3>

54 <p>A library has 15 copies of one book and 65 copies of another. They want to arrange them in shelves with the same number of books on each shelf, using the largest possible number of books per shelf. How many books will be in each shelf?</p>

53 <p>A library has 15 copies of one book and 65 copies of another. They want to arrange them in shelves with the same number of books on each shelf, using the largest possible number of books per shelf. How many books will be in each shelf?</p>

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

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

56 <p>GCF of 15 and 65 5 So each shelf will have 5 books.</p>

55 <p>GCF of 15 and 65 5 So each shelf will have 5 books.</p>

57 <h3>Explanation</h3>

56 <h3>Explanation</h3>

58 <p>There are 15 copies of one book and 65 copies of another.</p>

57 <p>There are 15 copies of one book and 65 copies of another.</p>

59 <p>To find the total number of books on each shelf, we should find the GCF of 15 and 65.</p>

58 <p>To find the total number of books on each shelf, we should find the GCF of 15 and 65.</p>

60 <p>There will be 5 books in each shelf.</p>

59 <p>There will be 5 books in each shelf.</p>

61 <p>Well explained 👍</p>

60 <p>Well explained 👍</p>

62 <h3>Problem 3</h3>

61 <h3>Problem 3</h3>

63 <p>A chef has 15 kg of flour and 65 kg of sugar. She wants to pack them in bags of equal weight, using the heaviest possible weight for each bag. What should be the weight of each bag?</p>

62 <p>A chef has 15 kg of flour and 65 kg of sugar. She wants to pack them in bags of equal weight, using the heaviest possible weight for each bag. What should be the weight of each bag?</p>

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

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

65 <p>For calculating the heaviest equal weight, we have to calculate the GCF of 15 and 65</p>

64 <p>For calculating the heaviest equal weight, we have to calculate the GCF of 15 and 65</p>

66 <p>The GCF of 15 and 65 5</p>

65 <p>The GCF of 15 and 65 5</p>

67 <p>The weight of each bag is 5 kg.</p>

66 <p>The weight of each bag is 5 kg.</p>

68 <h3>Explanation</h3>

67 <h3>Explanation</h3>

69 <p>For calculating the heaviest weight of the bags, first, we need to calculate the GCF of 15 and 65 which is 5.</p>

68 <p>For calculating the heaviest weight of the bags, first, we need to calculate the GCF of 15 and 65 which is 5.</p>

70 <p>The weight of each bag will be 5 kg.</p>

69 <p>The weight of each bag will be 5 kg.</p>

71 <p>Well explained 👍</p>

70 <p>Well explained 👍</p>

72 <h3>Problem 4</h3>

71 <h3>Problem 4</h3>

73 <p>A carpenter has two wooden beams, one 15 cm long and the other 65 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>

72 <p>A carpenter has two wooden beams, one 15 cm long and the other 65 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>

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

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

75 <p>The carpenter needs the longest piece of wood GCF of 15 and 65 5</p>

74 <p>The carpenter needs the longest piece of wood GCF of 15 and 65 5</p>

76 <p>The longest length of each piece is 5 cm.</p>

75 <p>The longest length of each piece is 5 cm.</p>

77 <h3>Explanation</h3>

76 <h3>Explanation</h3>

78 <p>To find the longest length of each piece of the two wooden beams, 15 cm and 65 cm, respectively.</p>

77 <p>To find the longest length of each piece of the two wooden beams, 15 cm and 65 cm, respectively.</p>

79 <p>We have to find the GCF of 15 and 65, which is 5 cm.</p>

78 <p>We have to find the GCF of 15 and 65, which is 5 cm.</p>

80 <p>The longest length of each piece is 5 cm.</p>

79 <p>The longest length of each piece is 5 cm.</p>

81 <p>Well explained 👍</p>

80 <p>Well explained 👍</p>

82 <h3>Problem 5</h3>

81 <h3>Problem 5</h3>

83 <p>If the GCF of 15 and ‘b’ is 5, and the LCM is 195. Find ‘b’.</p>

82 <p>If the GCF of 15 and ‘b’ is 5, and the LCM is 195. Find ‘b’.</p>

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

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

85 <p>The value of ‘b’ is 65.</p>

84 <p>The value of ‘b’ is 65.</p>

86 <h3>Explanation</h3>

85 <h3>Explanation</h3>

87 <p>GCF x LCM = product of the numbers</p>

86 <p>GCF x LCM = product of the numbers</p>

88 <p>5 × 195 = 15 × b</p>

87 <p>5 × 195 = 15 × b</p>

89 <p>975 = 15b</p>

88 <p>975 = 15b</p>

90 <p>b = 975 ÷ 15 = 65</p>

89 <p>b = 975 ÷ 15 = 65</p>

91 <p>Well explained 👍</p>

90 <p>Well explained 👍</p>

92 <h2>FAQs on the Greatest Common Factor of 15 and 65</h2>

91 <h2>FAQs on the Greatest Common Factor of 15 and 65</h2>

93 <h3>1.What is the LCM of 15 and 65?</h3>

92 <h3>1.What is the LCM of 15 and 65?</h3>

94 <p>The LCM of 15 and 65 is 195.</p>

93 <p>The LCM of 15 and 65 is 195.</p>

95 <h3>2.Is 15 divisible by 3?</h3>

94 <h3>2.Is 15 divisible by 3?</h3>

96 <p>Yes, 15 is divisible by 3 because the<a>sum</a>of its digits (1 + 5 = 6) is divisible by 3.</p>

95 <p>Yes, 15 is divisible by 3 because the<a>sum</a>of its digits (1 + 5 = 6) is divisible by 3.</p>

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

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

98 <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>

97 <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>

99 <h3>4.What is the prime factorization of 65?</h3>

98 <h3>4.What is the prime factorization of 65?</h3>

100 <p>The prime factorization of 65 is 5 x 13.</p>

99 <p>The prime factorization of 65 is 5 x 13.</p>

101 <h3>5.Are 15 and 65 prime numbers?</h3>

100 <h3>5.Are 15 and 65 prime numbers?</h3>

102 <p>No, 15 and 65 are not prime numbers because both of them have more than two factors.</p>

101 <p>No, 15 and 65 are not prime numbers because both of them have more than two factors.</p>

103 <h2>Important Glossaries for GCF of 15 and 65</h2>

102 <h2>Important Glossaries for GCF of 15 and 65</h2>

104 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.</li>

103 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.</li>

105 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, 25, and so on.</li>

104 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, 25, and so on.</li>

106 </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 65 are 5 and 13.</li>

105 </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 65 are 5 and 13.</li>

107 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 65 is divided by 15, the remainder is 5 and the quotient is 4.</li>

106 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 65 is divided by 15, the remainder is 5 and the quotient is 4.</li>

108 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 15 and 65 is 195.</li>

107 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 15 and 65 is 195.</li>

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

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

110 <p>▶</p>

109 <p>▶</p>

111 <h2>Hiralee Lalitkumar Makwana</h2>

110 <h2>Hiralee Lalitkumar Makwana</h2>

112 <h3>About the Author</h3>

111 <h3>About the Author</h3>

113 <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>

112 <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>

114 <h3>Fun Fact</h3>

113 <h3>Fun Fact</h3>

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

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