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1 - <p>159 Learners</p>

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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 the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 15 and 60.</p>

4 <h2>What is the GCF of 15 and 60?</h2>

5 <p>The<a>greatest common factor</a>of 15 and 60 is 15. 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 15 and 60?</h2>

7 <p>To find the GCF of 15 and 60, 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 15 and 60 by Using Listing of factors</h2>

12 <p>Steps to find the GCF of 15 and 60 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 15 = 1, 3, 5, 15.</p>

15 <p>Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 15 and 60: 1, 3, 5, 15.</p>

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

18 <p>The largest factor that both numbers have is 15.</p>

19 <p>The GCF of 15 and 60 is 15.</p>

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22 <h2>GCF of 15 and 60 Using Prime Factorization</h2>

21 <h2>GCF of 15 and 60 Using Prime Factorization</h2>

23 <p>To find the GCF of 15 and 60 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 15 and 60 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 15: 15 = 3 x 5</p>

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

26 <p>Prime Factors of 60: 60 = 2 x 2 x 3 x 5 = 2² x 3 x 5</p>

25 <p>Prime Factors of 60: 60 = 2 x 2 x 3 x 5 = 2² x 3 x 5</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: 3 x 5</p>

27 <p>The common prime factors are: 3 x 5</p>

29 <p><strong>Step 3:</strong>Multiply the common prime factors 3 x 5 = 15.</p>

28 <p><strong>Step 3:</strong>Multiply the common prime factors 3 x 5 = 15.</p>

30 <p>The Greatest Common Factor of 15 and 60 is 15.</p>

29 <p>The Greatest Common Factor of 15 and 60 is 15.</p>

31 <h2>GCF of 15 and 60 Using Division Method or Euclidean Algorithm Method</h2>

30 <h2>GCF of 15 and 60 Using Division Method or Euclidean Algorithm Method</h2>

32 <p>Find the GCF of 15 and 60 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

31 <p>Find the GCF of 15 and 60 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 60 by 15 60 ÷ 15 = 4 (<a>quotient</a>),</p>

33 <p>Here, divide 60 by 15 60 ÷ 15 = 4 (<a>quotient</a>),</p>

35 <p>The<a>remainder</a>is calculated as 60 - (15×4) = 0</p>

34 <p>The<a>remainder</a>is calculated as 60 - (15×4) = 0</p>

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

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

37 <p>The GCF of 15 and 60 is 15.</p>

36 <p>The GCF of 15 and 60 is 15.</p>

38 <h2>Common Mistakes and How to Avoid Them in GCF of 15 and 60</h2>

37 <h2>Common Mistakes and How to Avoid Them in GCF of 15 and 60</h2>

39 <p>Finding GCF of 15 and 60 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

38 <p>Finding GCF of 15 and 60 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

40 <h3>Problem 1</h3>

39 <h3>Problem 1</h3>

41 <p>A gardener has 15 rose bushes and 60 tulip bulbs. She 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>

40 <p>A gardener has 15 rose bushes and 60 tulip bulbs. She 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>Okay, lets begin</p>

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

43 <p>We should find GCF of 15 and 60 GCF of 15 and 60 3 x 5 = 15.</p>

42 <p>We should find GCF of 15 and 60 GCF of 15 and 60 3 x 5 = 15.</p>

44 <p>There are 15 equal groups 15 ÷ 15 = 1 60 ÷ 15 = 4</p>

43 <p>There are 15 equal groups 15 ÷ 15 = 1 60 ÷ 15 = 4</p>

45 <p>There will be 15 groups, and each group gets 1 rose bush and 4 tulip bulbs.</p>

44 <p>There will be 15 groups, and each group gets 1 rose bush and 4 tulip bulbs.</p>

46 <h3>Explanation</h3>

45 <h3>Explanation</h3>

47 <p>As the GCF of 15 and 60 is 15, the gardener can make 15 groups. Now divide 15 and 60 by 15. Each group gets 1 rose bush and 4 tulip bulbs.</p>

46 <p>As the GCF of 15 and 60 is 15, the gardener can make 15 groups. Now divide 15 and 60 by 15. Each group gets 1 rose bush and 4 tulip bulbs.</p>

48 <p>Well explained 👍</p>

47 <p>Well explained 👍</p>

49 <h3>Problem 2</h3>

48 <h3>Problem 2</h3>

50 <p>A school has 15 basketballs and 60 soccer balls. They want to arrange them in rows with the same number of balls in each row, using the largest possible number of balls per row. How many balls will be in each row?</p>

49 <p>A school has 15 basketballs and 60 soccer balls. They want to arrange them in rows with the same number of balls in each row, using the largest possible number of balls per row. How many balls will be in each row?</p>

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

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

52 <p>GCF of 15 and 60 3 x 5 = 15.</p>

51 <p>GCF of 15 and 60 3 x 5 = 15.</p>

53 <p>So each row will have 15 balls.</p>

52 <p>So each row will have 15 balls.</p>

54 <h3>Explanation</h3>

53 <h3>Explanation</h3>

55 <p>There are 15 basketballs and 60 soccer balls. To find the total number of balls in each row, we should find the GCF of 15 and 60. There will be 15 balls in each row.</p>

54 <p>There are 15 basketballs and 60 soccer balls. To find the total number of balls in each row, we should find the GCF of 15 and 60. There will be 15 balls in each row.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 3</h3>

56 <h3>Problem 3</h3>

58 <p>A tailor has 15 meters of silk fabric and 60 meters of cotton 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>

57 <p>A tailor has 15 meters of silk fabric and 60 meters of cotton 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>

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

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

60 <p>For calculating the longest equal length, we have to calculate the GCF of 15 and 60</p>

59 <p>For calculating the longest equal length, we have to calculate the GCF of 15 and 60</p>

61 <p>The GCF of 15 and 60 3 x 5 = 15.</p>

60 <p>The GCF of 15 and 60 3 x 5 = 15.</p>

62 <p>The fabric is 15 meters long.</p>

61 <p>The fabric is 15 meters long.</p>

63 <h3>Explanation</h3>

62 <h3>Explanation</h3>

64 <p>For calculating the longest length of the fabric first we need to calculate the GCF of 15 and 60 which is 15. The length of each piece of fabric will be 15 meters.</p>

63 <p>For calculating the longest length of the fabric first we need to calculate the GCF of 15 and 60 which is 15. The length of each piece of fabric will be 15 meters.</p>

65 <p>Well explained 👍</p>

64 <p>Well explained 👍</p>

66 <h3>Problem 4</h3>

65 <h3>Problem 4</h3>

67 <p>A carpenter has two wooden planks, one 15 cm long and the other 60 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>

66 <p>A carpenter has two wooden planks, one 15 cm long and the other 60 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>

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

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

69 <p>The carpenter needs the longest piece of wood GCF of 15 and 60 3 x 5 = 15.</p>

68 <p>The carpenter needs the longest piece of wood GCF of 15 and 60 3 x 5 = 15.</p>

70 <p>The longest length of each piece is 15 cm.</p>

69 <p>The longest length of each piece is 15 cm.</p>

71 <h3>Explanation</h3>

70 <h3>Explanation</h3>

72 <p>To find the longest length of each piece of the two wooden planks, 15 cm and 60 cm, respectively. We have to find the GCF of 15 and 60, which is 15 cm. The longest length of each piece is 15 cm.</p>

71 <p>To find the longest length of each piece of the two wooden planks, 15 cm and 60 cm, respectively. We have to find the GCF of 15 and 60, which is 15 cm. The longest length of each piece is 15 cm.</p>

73 <p>Well explained 👍</p>

72 <p>Well explained 👍</p>

74 <h3>Problem 5</h3>

73 <h3>Problem 5</h3>

75 <p>If the GCF of 15 and ‘b’ is 15, and the LCM is 60. Find ‘b’.</p>

74 <p>If the GCF of 15 and ‘b’ is 15, and the LCM is 60. Find ‘b’.</p>

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

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

77 <p>The value of ‘b’ is 60.</p>

76 <p>The value of ‘b’ is 60.</p>

78 <h3>Explanation</h3>

77 <h3>Explanation</h3>

79 <p>GCF x LCM = product of the numbers 15 × 60 = 15 × b</p>

78 <p>GCF x LCM = product of the numbers 15 × 60 = 15 × b</p>

80 <p>900 = 15b</p>

79 <p>900 = 15b</p>

81 <p>b = 900 ÷ 15 = 60</p>

80 <p>b = 900 ÷ 15 = 60</p>

82 <p>Well explained 👍</p>

81 <p>Well explained 👍</p>

83 <h2>FAQs on the Greatest Common Factor of 15 and 60</h2>

82 <h2>FAQs on the Greatest Common Factor of 15 and 60</h2>

84 <h3>1.What is the LCM of 15 and 60?</h3>

83 <h3>1.What is the LCM of 15 and 60?</h3>

85 <p>The LCM of 15 and 60 is 60.</p>

84 <p>The LCM of 15 and 60 is 60.</p>

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

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

87 <p>Yes, 15 is divisible by 3 because 15 ÷ 3 = 5 with no remainder.</p>

86 <p>Yes, 15 is divisible by 3 because 15 ÷ 3 = 5 with no remainder.</p>

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

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

89 <p>The only common factor of<a>prime numbers</a>is 1, so the GCF of any two prime numbers is 1.</p>

88 <p>The only common factor of<a>prime numbers</a>is 1, so the GCF of any two prime numbers is 1.</p>

90 <h3>4.What is the prime factorization of 60?</h3>

89 <h3>4.What is the prime factorization of 60?</h3>

91 <p>The prime factorization of 60 is 2² x 3 x 5.</p>

90 <p>The prime factorization of 60 is 2² x 3 x 5.</p>

92 <h3>5.Are 15 and 60 prime numbers?</h3>

91 <h3>5.Are 15 and 60 prime numbers?</h3>

93 <p>No, 15 and 60 are not prime numbers because both of them have more than two factors.</p>

92 <p>No, 15 and 60 are not prime numbers because both of them have more than two factors.</p>

94 <h2>Important Glossaries for GCF of 15 and 60</h2>

93 <h2>Important Glossaries for GCF of 15 and 60</h2>

95 <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>

94 <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>

96 <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, and so on.</li>

95 <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, and so on.</li>

97 <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 60 are 2, 3, and 5.</li>

96 <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 60 are 2, 3, and 5.</li>

98 <li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 17 is divided by 5, the remainder is 2 and the quotient is 3.</li>

97 <li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 17 is divided by 5, the remainder is 2 and the quotient is 3.</li>

99 <li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 15 and 60 is 60.</li>

98 <li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 15 and 60 is 60.</li>

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

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

101 <p>▶</p>

100 <p>▶</p>

102 <h2>Hiralee Lalitkumar Makwana</h2>

101 <h2>Hiralee Lalitkumar Makwana</h2>

103 <h3>About the Author</h3>

102 <h3>About the Author</h3>

104 <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>

103 <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>

105 <h3>Fun Fact</h3>

104 <h3>Fun Fact</h3>

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

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