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2 <p>Last updated on<strong>September 11, 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, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 21 and 70.</p>

4 <h2>What is the GCF of 21 and 70?</h2>

5 <p>The<a>greatest common factor</a>of 21 and 70 is 7. 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 21 and 70?</h2>

7 <p>To find the GCF of 21 and 70, a few methods are described below -</p>

8 <ol><li>Listing Factors</li>

9 <li>Prime Factorization</li>

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

11 </ol><h2>GCF of 21 and 70 by Using Listing of factors</h2>

12 <p>Steps to find the GCF of 21 and 70 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 21 = 1, 3, 7, 21.</p>

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

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 21 and 70: 1, 7.</p>

17 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 7.</p>

18 <p>The GCF of 21 and 70 is 7.</p>

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

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

22 <p>To find the GCF of 21 and 70 using the Prime Factorization Method, follow these steps:</p>

21 <p>To find the GCF of 21 and 70 using the Prime Factorization Method, follow these steps:</p>

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

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

24 <p>Prime Factors of 21: 21 = 3 x 7</p>

23 <p>Prime Factors of 21: 21 = 3 x 7</p>

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

24 <p>Prime Factors of 70: 70 = 2 x 5 x 7</p>

26 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 7</p>

25 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 7</p>

27 <p><strong>Step 3:</strong>Multiply the common prime factors 7 = 7 The Greatest Common Factor of 21 and 70 is 7.</p>

26 <p><strong>Step 3:</strong>Multiply the common prime factors 7 = 7 The Greatest Common Factor of 21 and 70 is 7.</p>

28 <h2>GCF of 21 and 70 Using Division Method or Euclidean Algorithm Method</h2>

27 <h2>GCF of 21 and 70 Using Division Method or Euclidean Algorithm Method</h2>

29 <p>Find the GCF of 21 and 70 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

28 <p>Find the GCF of 21 and 70 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

30 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 70 by 21 70 ÷ 21 = 3 (<a>quotient</a>), The<a>remainder</a>is calculated as 70 - (21×3) = 7</p>

29 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 70 by 21 70 ÷ 21 = 3 (<a>quotient</a>), The<a>remainder</a>is calculated as 70 - (21×3) = 7</p>

31 <p>The remainder is 7, not zero, so continue the process</p>

30 <p>The remainder is 7, not zero, so continue the process</p>

32 <p><strong>Step 2:</strong>Now divide the previous divisor (21) by the previous remainder (7) Divide 21 by 7 21 ÷ 7 = 3 (quotient), remainder = 21 - (7×3) = 0</p>

31 <p><strong>Step 2:</strong>Now divide the previous divisor (21) by the previous remainder (7) Divide 21 by 7 21 ÷ 7 = 3 (quotient), remainder = 21 - (7×3) = 0</p>

33 <p>The remainder is zero, the divisor will become the GCF. The GCF of 21 and 70 is 7.</p>

32 <p>The remainder is zero, the divisor will become the GCF. The GCF of 21 and 70 is 7.</p>

34 <h2>Common Mistakes and How to Avoid Them in GCF of 21 and 70</h2>

33 <h2>Common Mistakes and How to Avoid Them in GCF of 21 and 70</h2>

35 <p>Finding GCF of 21 and 70 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.</p>

34 <p>Finding GCF of 21 and 70 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.</p>

36 <h3>Problem 1</h3>

35 <h3>Problem 1</h3>

37 <p>A teacher has 21 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>

36 <p>A teacher has 21 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>

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

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

39 <p>We should find the GCF of 21 and 70 GCF of 21 and 70 is 7.</p>

38 <p>We should find the GCF of 21 and 70 GCF of 21 and 70 is 7.</p>

40 <p>There are 7 equal groups 21 ÷ 7 = 3 70 ÷ 7 = 10</p>

39 <p>There are 7 equal groups 21 ÷ 7 = 3 70 ÷ 7 = 10</p>

41 <p>There will be 7 groups, and each group gets 3 apples and 10 oranges.</p>

40 <p>There will be 7 groups, and each group gets 3 apples and 10 oranges.</p>

42 <h3>Explanation</h3>

41 <h3>Explanation</h3>

43 <p>As the GCF of 21 and 70 is 7, the teacher can make 7 groups.</p>

42 <p>As the GCF of 21 and 70 is 7, the teacher can make 7 groups.</p>

44 <p>Now divide 21 and 70 by 7. Each group gets 3 apples and 10 oranges.</p>

43 <p>Now divide 21 and 70 by 7. Each group gets 3 apples and 10 oranges.</p>

45 <p>Well explained 👍</p>

44 <p>Well explained 👍</p>

46 <h3>Problem 2</h3>

45 <h3>Problem 2</h3>

47 <p>A school has 21 desks and 70 chairs. They want to arrange them in rows with the same number of desks and chairs in each row, using the largest possible number of items per row. How many items will be in each row?</p>

46 <p>A school has 21 desks and 70 chairs. They want to arrange them in rows with the same number of desks and chairs in each row, using the largest possible number of items per row. How many items will be in each row?</p>

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

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

49 <p>GCF of 21 and 70 is 7. So each row will have 7 items.</p>

48 <p>GCF of 21 and 70 is 7. So each row will have 7 items.</p>

50 <h3>Explanation</h3>

49 <h3>Explanation</h3>

51 <p>There are 21 desks and 70 chairs. To find the total number of items in each row, we should find the GCF of 21 and 70. There will be 7 items in each row.</p>

50 <p>There are 21 desks and 70 chairs. To find the total number of items in each row, we should find the GCF of 21 and 70. There will be 7 items in each row.</p>

52 <p>Well explained 👍</p>

51 <p>Well explained 👍</p>

53 <h3>Problem 3</h3>

52 <h3>Problem 3</h3>

54 <p>A tailor has 21 meters of red fabric and 70 meters of blue 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>

53 <p>A tailor has 21 meters of red fabric and 70 meters of blue 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>

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

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

56 <p>For calculating the longest equal length, we have to calculate the GCF of 21 and 70</p>

55 <p>For calculating the longest equal length, we have to calculate the GCF of 21 and 70</p>

57 <p>The GCF of 21 and 70 is 7. The length of each piece is 7 meters.</p>

56 <p>The GCF of 21 and 70 is 7. The length of each piece is 7 meters.</p>

58 <h3>Explanation</h3>

57 <h3>Explanation</h3>

59 <p>For calculating the longest length of the fabric, first we need to calculate the GCF of 21 and 70, which is 7. The length of each piece of fabric will be 7 meters.</p>

58 <p>For calculating the longest length of the fabric, first we need to calculate the GCF of 21 and 70, which is 7. The length of each piece of fabric will be 7 meters.</p>

60 <p>Well explained 👍</p>

59 <p>Well explained 👍</p>

61 <h3>Problem 4</h3>

60 <h3>Problem 4</h3>

62 <p>A carpenter has two wooden planks, one 21 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>

61 <p>A carpenter has two wooden planks, one 21 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>

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

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

64 <p>The carpenter needs the longest piece of wood GCF of 21 and 70 is 7.</p>

63 <p>The carpenter needs the longest piece of wood GCF of 21 and 70 is 7.</p>

65 <p>The longest length of each piece is 7 cm.</p>

64 <p>The longest length of each piece is 7 cm.</p>

66 <h3>Explanation</h3>

65 <h3>Explanation</h3>

67 <p>To find the longest length of each piece of the two wooden planks, 21 cm and 70 cm, respectively, we have to find the GCF of 21 and 70, which is 7 cm. The longest length of each piece is 7 cm.</p>

66 <p>To find the longest length of each piece of the two wooden planks, 21 cm and 70 cm, respectively, we have to find the GCF of 21 and 70, which is 7 cm. The longest length of each piece is 7 cm.</p>

68 <p>Well explained 👍</p>

67 <p>Well explained 👍</p>

69 <h3>Problem 5</h3>

68 <h3>Problem 5</h3>

70 <p>If the GCF of 21 and ‘a’ is 7, and the LCM is 210. Find ‘a’.</p>

69 <p>If the GCF of 21 and ‘a’ is 7, and the LCM is 210. Find ‘a’.</p>

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

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

72 <p>The value of ‘a’ is 70.</p>

71 <p>The value of ‘a’ is 70.</p>

73 <h3>Explanation</h3>

72 <h3>Explanation</h3>

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

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

75 <p>7 × 210 = 21 × a</p>

74 <p>7 × 210 = 21 × a</p>

76 <p>1470 = 21a</p>

75 <p>1470 = 21a</p>

77 <p>a = 1470 ÷ 21 = 70</p>

76 <p>a = 1470 ÷ 21 = 70</p>

78 <p>Well explained 👍</p>

77 <p>Well explained 👍</p>

79 <h2>FAQs on the Greatest Common Factor of 21 and 70</h2>

78 <h2>FAQs on the Greatest Common Factor of 21 and 70</h2>

80 <h3>1.What is the LCM of 21 and 70?</h3>

79 <h3>1.What is the LCM of 21 and 70?</h3>

81 <p>The LCM of 21 and 70 is 210.</p>

80 <p>The LCM of 21 and 70 is 210.</p>

82 <h3>2.Is 21 divisible by 3?</h3>

81 <h3>2.Is 21 divisible by 3?</h3>

83 <p>Yes, 21 is divisible by 3 because 3 is one of its factors.</p>

82 <p>Yes, 21 is divisible by 3 because 3 is one of its factors.</p>

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

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

85 <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>

84 <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>

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

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

87 <p>The prime factorization of 70 is 2 x 5 x 7.</p>

86 <p>The prime factorization of 70 is 2 x 5 x 7.</p>

88 <h3>5.Are 21 and 70 prime numbers?</h3>

87 <h3>5.Are 21 and 70 prime numbers?</h3>

89 <p>No, 21 and 70 are not prime numbers because both of them have more than two factors.</p>

88 <p>No, 21 and 70 are not prime numbers because both of them have more than two factors.</p>

90 <h2>Important Glossaries for GCF of 21 and 70</h2>

89 <h2>Important Glossaries for GCF of 21 and 70</h2>

91 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 7 are 1 and 7.</li>

90 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 7 are 1 and 7.</li>

92 </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 21 are 3 and 7.</li>

91 </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 21 are 3 and 7.</li>

93 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 70 is divided by 21, the remainder is 7 and the quotient is 3.</li>

92 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 70 is divided by 21, the remainder is 7 and the quotient is 3.</li>

94 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 21 and 70 is 210.</li>

93 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 21 and 70 is 210.</li>

95 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 21 and 70 is 7, as it is their largest common factor that divides the numbers completely.</li>

94 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 21 and 70 is 7, as it is their largest common factor that divides the numbers completely.</li>

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

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

97 <p>▶</p>

96 <p>▶</p>

98 <h2>Hiralee Lalitkumar Makwana</h2>

97 <h2>Hiralee Lalitkumar Makwana</h2>

99 <h3>About the Author</h3>

98 <h3>About the Author</h3>

100 <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>

99 <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>

101 <h3>Fun Fact</h3>

100 <h3>Fun Fact</h3>

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

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