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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 60 and 75.</p>

4 <h2>What is the GCF of 60 and 75?</h2>

5 <p>The<a>greatest common factor</a>of 60 and 75 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, which are always positive.</p>

6 <h2>How to find the GCF of 60 and 75?</h2>

7 <p>To find the GCF of 60 and 75, a few methods are described below:</p>

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

9 </ul><ul><li>Prime Factorization</li>

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

11 </ul><h3>GCF of 60 and 75 by Using Listing of Factors</h3>

12 <p>Steps to find the GCF of 60 and 75 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 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.</p>

15 <p>Factors of 75 = 1, 3, 5, 15, 25, 75.</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them.</p>

17 <p>Common factors of 60 and 75: 1, 3, 5, 15.</p>

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

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

20 <p>The GCF of 60 and 75 is 15.</p>

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23 <h3>GCF of 60 and 75 Using Prime Factorization</h3>

22 <h3>GCF of 60 and 75 Using Prime Factorization</h3>

24 <p>To find the GCF of 60 and 75 using the Prime Factorization Method, follow these steps:</p>

23 <p>To find the GCF of 60 and 75 using the Prime Factorization Method, follow these steps:</p>

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

24 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number:</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>Prime Factors of 75: 75 = 3 x 5 x 5 = 3 x 52</p>

26 <p>Prime Factors of 75: 75 = 3 x 5 x 5 = 3 x 52</p>

28 <p><strong>Step 2:</strong>Now, identify the common prime factors. The common prime factors are: 3 x 5</p>

27 <p><strong>Step 2:</strong>Now, identify the common prime factors. 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 60 and 75 is 15.</p>

29 <p>The Greatest Common Factor of 60 and 75 is 15.</p>

31 <h3>GCF of 60 and 75 Using Division Method or Euclidean Algorithm Method</h3>

30 <h3>GCF of 60 and 75 Using Division Method or Euclidean Algorithm Method</h3>

32 <p>Find the GCF of 60 and 75 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

31 <p>Find the GCF of 60 and 75 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 75 by 60 75 ÷ 60 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 75 - (60×1) = 15</p>

33 <p>Here, divide 75 by 60 75 ÷ 60 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 75 - (60×1) = 15</p>

35 <p>The remainder is 15, not zero, so continue the process</p>

34 <p>The remainder is 15, not zero, so continue the process</p>

36 <p><strong>Step 2:</strong>Now divide the previous divisor (60) by the previous remainder (15)</p>

35 <p><strong>Step 2:</strong>Now divide the previous divisor (60) by the previous remainder (15)</p>

37 <p>Divide 60 by 15 60 ÷ 15 = 4 (quotient), remainder = 60 - (15×4) = 0</p>

36 <p>Divide 60 by 15 60 ÷ 15 = 4 (quotient), remainder = 60 - (15×4) = 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 60 and 75 is 15.</p>

38 <p>The GCF of 60 and 75 is 15.</p>

40 <h2>Common Mistakes and How to Avoid Them in GCF of 60 and 75</h2>

39 <h2>Common Mistakes and How to Avoid Them in GCF of 60 and 75</h2>

41 <p>Finding GCF of 60 and 75 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 GCF of 60 and 75 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 60 tulips and 75 roses. He wants to plant them in rows with the same number of flowers in each row, using the largest possible number of flowers per row. How many flowers will be in each row?</p>

42 <p>A gardener has 60 tulips and 75 roses. He wants to plant them in rows with the same number of flowers in each row, using the largest possible number of flowers per row. How many flowers will be in each row?</p>

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

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

45 <p>We should find the GCF of 60 and 75 GCF of 60 and 75</p>

44 <p>We should find the GCF of 60 and 75 GCF of 60 and 75</p>

46 <p>3 x 5 = 15.</p>

45 <p>3 x 5 = 15.</p>

47 <p>There are 15 equal rows</p>

46 <p>There are 15 equal rows</p>

48 <p>60 ÷ 15 = 4</p>

47 <p>60 ÷ 15 = 4</p>

49 <p>75 ÷ 15 = 5</p>

48 <p>75 ÷ 15 = 5</p>

50 <p>There will be 15 rows, and each row gets 4 tulips and 5 roses.</p>

49 <p>There will be 15 rows, and each row gets 4 tulips and 5 roses.</p>

51 <h3>Explanation</h3>

50 <h3>Explanation</h3>

52 <p>As the GCF of 60 and 75 is 15, the gardener can make 15 rows.</p>

51 <p>As the GCF of 60 and 75 is 15, the gardener can make 15 rows.</p>

53 <p>Now divide 60 and 75 by 15.</p>

52 <p>Now divide 60 and 75 by 15.</p>

54 <p>Each row gets 4 tulips and 5 roses.</p>

53 <p>Each row gets 4 tulips and 5 roses.</p>

55 <p>Well explained 👍</p>

54 <p>Well explained 👍</p>

56 <h3>Problem 2</h3>

55 <h3>Problem 2</h3>

57 <p>A school has 60 desks and 75 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>

56 <p>A school has 60 desks and 75 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>

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

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

59 <p>GCF of 60 and 75 3 x 5 = 15. So each row will have 15 items.</p>

58 <p>GCF of 60 and 75 3 x 5 = 15. So each row will have 15 items.</p>

60 <h3>Explanation</h3>

59 <h3>Explanation</h3>

61 <p>There are 60 desks and 75 chairs.</p>

60 <p>There are 60 desks and 75 chairs.</p>

62 <p>To find the total number of items in each row, we should find the GCF of 60 and 75.</p>

61 <p>To find the total number of items in each row, we should find the GCF of 60 and 75.</p>

63 <p>There will be 15 items in each row.</p>

62 <p>There will be 15 items in each row.</p>

64 <p>Well explained 👍</p>

63 <p>Well explained 👍</p>

65 <h3>Problem 3</h3>

64 <h3>Problem 3</h3>

66 <p>A tailor has 60 meters of green fabric and 75 meters of yellow 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>

65 <p>A tailor has 60 meters of green fabric and 75 meters of yellow 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>

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

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

68 <p>For calculating the longest equal length, we have to calculate the GCF of 60 and 75</p>

67 <p>For calculating the longest equal length, we have to calculate the GCF of 60 and 75</p>

69 <p>The GCF of 60 and 75</p>

68 <p>The GCF of 60 and 75</p>

70 <p>3 x 5 = 15.</p>

69 <p>3 x 5 = 15.</p>

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

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

72 <h3>Explanation</h3>

71 <h3>Explanation</h3>

73 <p>For calculating the longest length of the fabric first, we need to calculate the GCF of 60 and 75, which is 15. The length of each piece of the fabric will be 15 meters.</p>

72 <p>For calculating the longest length of the fabric first, we need to calculate the GCF of 60 and 75, which is 15. The length of each piece of the fabric will be 15 meters.</p>

74 <p>Well explained 👍</p>

73 <p>Well explained 👍</p>

75 <h3>Problem 4</h3>

74 <h3>Problem 4</h3>

76 <p>A carpenter has two wooden planks, one 60 cm long and the other 75 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>

75 <p>A carpenter has two wooden planks, one 60 cm long and the other 75 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>

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

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

78 <p>The carpenter needs the longest piece of wood GCF of 60 and 75</p>

77 <p>The carpenter needs the longest piece of wood GCF of 60 and 75</p>

79 <p>3 x 5 = 15.</p>

78 <p>3 x 5 = 15.</p>

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

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

81 <h3>Explanation</h3>

80 <h3>Explanation</h3>

82 <p>To find the longest length of each piece of the two wooden planks, 60 cm and 75 cm, respectively.</p>

81 <p>To find the longest length of each piece of the two wooden planks, 60 cm and 75 cm, respectively.</p>

83 <p>We have to find the GCF of 60 and 75, which is 15 cm.</p>

82 <p>We have to find the GCF of 60 and 75, which is 15 cm.</p>

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

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

85 <p>Well explained 👍</p>

84 <p>Well explained 👍</p>

86 <h3>Problem 5</h3>

85 <h3>Problem 5</h3>

87 <p>If the GCF of 60 and ‘b’ is 15, and the LCM is 300. Find ‘b’.</p>

86 <p>If the GCF of 60 and ‘b’ is 15, and the LCM is 300. Find ‘b’.</p>

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

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

89 <p>The value of ‘b’ is 75.</p>

88 <p>The value of ‘b’ is 75.</p>

90 <h3>Explanation</h3>

89 <h3>Explanation</h3>

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

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

92 <p>15 × 300 = 60 × b</p>

91 <p>15 × 300 = 60 × b</p>

93 <p>4500 = 60b</p>

92 <p>4500 = 60b</p>

94 <p>b = 4500 ÷ 60 = 75</p>

93 <p>b = 4500 ÷ 60 = 75</p>

95 <p>Well explained 👍</p>

94 <p>Well explained 👍</p>

96 <h2>FAQs on the Greatest Common Factor of 60 and 75</h2>

95 <h2>FAQs on the Greatest Common Factor of 60 and 75</h2>

97 <h3>1.What is the LCM of 60 and 75?</h3>

96 <h3>1.What is the LCM of 60 and 75?</h3>

98 <p>The LCM of 60 and 75 is 300.</p>

97 <p>The LCM of 60 and 75 is 300.</p>

99 <h3>2.Is 60 divisible by 2?</h3>

98 <h3>2.Is 60 divisible by 2?</h3>

100 <p>Yes, 60 is divisible by 2 because it is an even number.</p>

99 <p>Yes, 60 is divisible by 2 because it is an even number.</p>

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

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

102 <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>

101 <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>

103 <h3>4.What is the prime factorization of 75?</h3>

102 <h3>4.What is the prime factorization of 75?</h3>

104 <p>The prime factorization of 75 is 3 x 5^2.</p>

103 <p>The prime factorization of 75 is 3 x 5^2.</p>

105 <h3>5.Are 60 and 75 prime numbers?</h3>

104 <h3>5.Are 60 and 75 prime numbers?</h3>

106 <p>No, 60 and 75 are not prime numbers because both of them have more than two factors.</p>

105 <p>No, 60 and 75 are not prime numbers because both of them have more than two factors.</p>

107 <h2>Important Glossaries for GCF of 60 and 75</h2>

106 <h2>Important Glossaries for GCF of 60 and 75</h2>

108 <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>

107 <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>

109 </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>

108 </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>

110 </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 30 are 2, 3, and 5.</li>

109 </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 30 are 2, 3, and 5.</li>

111 </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 4, the remainder is 2 and the quotient is 3.</li>

110 </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 4, the remainder is 2 and the quotient is 3.</li>

112 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 60 and 75 is 300.</li>

111 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 60 and 75 is 300.</li>

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

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

114 <p>▶</p>

113 <p>▶</p>

115 <h2>Hiralee Lalitkumar Makwana</h2>

114 <h2>Hiralee Lalitkumar Makwana</h2>

116 <h3>About the Author</h3>

115 <h3>About the Author</h3>

117 <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>

116 <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>

118 <h3>Fun Fact</h3>

117 <h3>Fun Fact</h3>

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

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