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1 - <p>125 Learners</p>

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2 <p>Last updated on<strong>September 19, 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 70.</p>

4 <h2>What is the GCF of 60 and 70?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>60 and 70 is 10. 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 60 and 70?</h2>

8 <p>To find the GCF of 60 and 70, 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 60 and 70 by Using Listing of factors</h2>

13 <p>Steps to find the GCF of 60 and 70 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 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.</p>

16 <p>Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70.</p>

17 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 60 and 70: 1, 2, 5, 10.</p>

18 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 10.</p>

19 <p>The GCF of 60 and 70 is 10.</p>

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22 <h2>GCF of 60 and 70 Using Prime Factorization</h2>

21 <h2>GCF of 60 and 70 Using Prime Factorization</h2>

23 <p>To find the GCF of 60 and 70 using the Prime Factorization Method, follow these steps:</p>

22 <p>To find the GCF of 60 and 70 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 60: 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5</p>

24 <p>Prime Factors of 60: 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5</p>

26 <p>Prime Factors of 70: 70 = 2 × 5 × 7 = 2 × 5 × 7</p>

25 <p>Prime Factors of 70: 70 = 2 × 5 × 7 = 2 × 5 × 7</p>

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

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

28 <p><strong>Step 3:</strong>Multiply the common prime factors 2 × 5 = 10.</p>

27 <p><strong>Step 3:</strong>Multiply the common prime factors 2 × 5 = 10.</p>

29 <p>The Greatest Common Factor of 60 and 70 is 10.</p>

28 <p>The Greatest Common Factor of 60 and 70 is 10.</p>

30 <h2>GCF of 60 and 70 Using Division Method or Euclidean Algorithm Method</h2>

29 <h2>GCF of 60 and 70 Using Division Method or Euclidean Algorithm Method</h2>

31 <p>Find the GCF of 60 and 70 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

30 <p>Find the GCF of 60 and 70 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 Here, divide 70 by 60 70 ÷ 60 = 1 (<a>quotient</a>),</p>

31 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 70 by 60 70 ÷ 60 = 1 (<a>quotient</a>),</p>

33 <p>The<a>remainder</a>is calculated as 70 - (60×1) = 10 The remainder is 10, not zero, so continue the process</p>

32 <p>The<a>remainder</a>is calculated as 70 - (60×1) = 10 The remainder is 10, not zero, so continue the process</p>

34 <p><strong>Step 2:</strong>Now divide the previous divisor (60) by the previous remainder (10)</p>

33 <p><strong>Step 2:</strong>Now divide the previous divisor (60) by the previous remainder (10)</p>

35 <p>Divide 60 by 10 60 ÷ 10 = 6 (quotient), remainder = 60 - (10×6) = 0</p>

34 <p>Divide 60 by 10 60 ÷ 10 = 6 (quotient), remainder = 60 - (10×6) = 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 60 and 70 is 10.</p>

36 <p>The GCF of 60 and 70 is 10.</p>

38 <h2>Common Mistakes and How to Avoid Them in GCF of 60 and 70</h2>

37 <h2>Common Mistakes and How to Avoid Them in GCF of 60 and 70</h2>

39 <p>Finding the GCF of 60 and 70 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 the GCF of 60 and 70 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 teacher has 60 apples and 70 oranges. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?</p>

40 <p>A teacher has 60 apples and 70 oranges. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?</p>

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

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

43 <p>We should find the GCF of 60 and 70 GCF of 60 and 70 2 × 5 = 10.</p>

42 <p>We should find the GCF of 60 and 70 GCF of 60 and 70 2 × 5 = 10.</p>

44 <p>There are 10 equal groups 60 ÷ 10 = 6 70 ÷ 10 = 7</p>

43 <p>There are 10 equal groups 60 ÷ 10 = 6 70 ÷ 10 = 7</p>

45 <p>There will be 10 groups, and each group gets 6 apples and 7 oranges.</p>

44 <p>There will be 10 groups, and each group gets 6 apples and 7 oranges.</p>

46 <h3>Explanation</h3>

45 <h3>Explanation</h3>

47 <p>As the GCF of 60 and 70 is 10, the teacher can make 10 groups.</p>

46 <p>As the GCF of 60 and 70 is 10, the teacher can make 10 groups.</p>

48 <p>Now divide 60 and 70 by 10.</p>

47 <p>Now divide 60 and 70 by 10.</p>

49 <p>Each group gets 6 apples and 7 oranges.</p>

48 <p>Each group gets 6 apples and 7 oranges.</p>

50 <p>Well explained 👍</p>

49 <p>Well explained 👍</p>

51 <h3>Problem 2</h3>

50 <h3>Problem 2</h3>

52 <p>A school has 60 red flags and 70 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?</p>

51 <p>A school has 60 red flags and 70 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?</p>

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

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

54 <p>GCF of 60 and 70 2 × 5 = 10. So each row will have 10 flags.</p>

53 <p>GCF of 60 and 70 2 × 5 = 10. So each row will have 10 flags.</p>

55 <h3>Explanation</h3>

54 <h3>Explanation</h3>

56 <p>There are 60 red and 70 blue flags. To find the total number of flags in each row, we should find the GCF of 60 and 70.</p>

55 <p>There are 60 red and 70 blue flags. To find the total number of flags in each row, we should find the GCF of 60 and 70.</p>

57 <p>There will be 10 flags in each row.</p>

56 <p>There will be 10 flags in each row.</p>

58 <p>Well explained 👍</p>

57 <p>Well explained 👍</p>

59 <h3>Problem 3</h3>

58 <h3>Problem 3</h3>

60 <p>A tailor has 60 meters of green fabric and 70 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>

59 <p>A tailor has 60 meters of green fabric and 70 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>

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

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

62 <p>For calculating the longest equal length, we have to calculate the GCF of 60 and 70</p>

61 <p>For calculating the longest equal length, we have to calculate the GCF of 60 and 70</p>

63 <p>The GCF of 60 and 70 2 × 5 = 10.</p>

62 <p>The GCF of 60 and 70 2 × 5 = 10.</p>

64 <p>The fabric is 10 meters long.</p>

63 <p>The fabric is 10 meters long.</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

66 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 60 and 70, which is 10.</p>

65 <p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 60 and 70, which is 10.</p>

67 <p>The length of each piece of the fabric will be 10 meters.</p>

66 <p>The length of each piece of the fabric will be 10 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 60 cm long and the other 70 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 60 cm long and the other 70 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 60 and 70 2 × 5 = 10.</p>

71 <p>The carpenter needs the longest piece of wood GCF of 60 and 70 2 × 5 = 10.</p>

73 <p>The longest length of each piece is 10 cm.</p>

72 <p>The longest length of each piece is 10 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, 60 cm and 70 cm, respectively, we have to find the GCF of 60 and 70, which is 10 cm.</p>

74 <p>To find the longest length of each piece of the two wooden planks, 60 cm and 70 cm, respectively, we have to find the GCF of 60 and 70, which is 10 cm.</p>

76 <p>The longest length of each piece is 10 cm.</p>

75 <p>The longest length of each piece is 10 cm.</p>

77 <p>Well explained 👍</p>

76 <p>Well explained 👍</p>

78 <h3>Problem 5</h3>

77 <h3>Problem 5</h3>

79 <p>If the GCF of 60 and ‘b’ is 10, and the LCM is 420. Find ‘b’.</p>

78 <p>If the GCF of 60 and ‘b’ is 10, and the LCM is 420. Find ‘b’.</p>

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

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

81 <p>The value of ‘b’ is 70.</p>

80 <p>The value of ‘b’ is 70.</p>

82 <h3>Explanation</h3>

81 <h3>Explanation</h3>

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

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

84 <p>10 × 420 = 60 × b</p>

83 <p>10 × 420 = 60 × b</p>

85 <p>4200 = 60b</p>

84 <p>4200 = 60b</p>

86 <p>b = 4200 ÷ 60 = 70</p>

85 <p>b = 4200 ÷ 60 = 70</p>

87 <p>Well explained 👍</p>

86 <p>Well explained 👍</p>

88 <h2>FAQs on the Greatest Common Factor of 60 and 70</h2>

87 <h2>FAQs on the Greatest Common Factor of 60 and 70</h2>

89 <h3>1.What is the LCM of 60 and 70?</h3>

88 <h3>1.What is the LCM of 60 and 70?</h3>

90 <p>The LCM of 60 and 70 is 420.</p>

89 <p>The LCM of 60 and 70 is 420.</p>

91 <h3>2.Is 60 divisible by 3?</h3>

90 <h3>2.Is 60 divisible by 3?</h3>

92 <p>Yes, 60 is divisible by 3 because the<a>sum</a>of its digits (6 + 0) is divisible by 3.</p>

91 <p>Yes, 60 is divisible by 3 because the<a>sum</a>of its digits (6 + 0) is divisible by 3.</p>

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

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

94 <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 <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>

95 <h3>4.What is the prime factorization of 70?</h3>

94 <h3>4.What is the prime factorization of 70?</h3>

96 <p>The prime factorization of 70 is 2 × 5 × 7.</p>

95 <p>The prime factorization of 70 is 2 × 5 × 7.</p>

97 <h3>5.Are 60 and 70 prime numbers?</h3>

96 <h3>5.Are 60 and 70 prime numbers?</h3>

98 <p>No, 60 and 70 are not prime numbers because both of them have more than two factors.</p>

97 <p>No, 60 and 70 are not prime numbers because both of them have more than two factors.</p>

99 <h2>Important Glossaries for GCF of 60 and 70</h2>

98 <h2>Important Glossaries for GCF of 60 and 70</h2>

100 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.</li>

99 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.</li>

101 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, and so on.</li>

100 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, and so on.</li>

102 </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>

101 </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>

103 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 9 is divided by 4, the remainder is 1 and the quotient is 2.</li>

102 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 9 is divided by 4, the remainder is 1 and the quotient is 2.</li>

104 </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 70 is 420.</li>

103 </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 70 is 420.</li>

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

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

106 <p>▶</p>

105 <p>▶</p>

107 <h2>Hiralee Lalitkumar Makwana</h2>

106 <h2>Hiralee Lalitkumar Makwana</h2>

108 <h3>About the Author</h3>

107 <h3>About the Author</h3>

109 <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>

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>

110 <h3>Fun Fact</h3>

109 <h3>Fun Fact</h3>

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

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