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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, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 6 and 21.</p>

4 <h2>What is the GCF of 6 and 21?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>6 and 21 is 3. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number.</p>

6 <p>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>

7 <h2>How to find the GCF of 6 and 21?</h2>

8 <p>To find the GCF of 6 and 21, a few methods are described below:</p>

9 <ol><li>Listing Factors</li>

10 <li>Prime Factorization</li>

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

12 </ol><h2>GCF of 6 and 21 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 6 and 21 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 6 = 1, 2, 3, 6.</p>

16 <p>Factors of 21 = 1, 3, 7, 21.</p>

17 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them. Common factors of 6 and 21: 1, 3.</p>

18 <p><strong>Step 3:</strong>Choose the largest factor. The largest factor that both numbers have is 3. The GCF of 6 and 21 is 3.</p>

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21 <h2>GCF of 6 and 21 Using Prime Factorization</h2>

20 <h2>GCF of 6 and 21 Using Prime Factorization</h2>

22 <p>To find the GCF of 6 and 21 using Prime Factorization Method, follow these steps:</p>

21 <p>To find the GCF of 6 and 21 using 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 6: 6 = 2 x 3</p>

23 <p>Prime factors of 6: 6 = 2 x 3</p>

25 <p>Prime factors of 21: 21 = 3 x 7</p>

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

26 <p><strong>Step 2:</strong>Now, identify the common prime factors. The common prime factor is: 3</p>

25 <p><strong>Step 2:</strong>Now, identify the common prime factors. The common prime factor is: 3</p>

27 <p><strong>Step 3:</strong>Multiply the common prime factors. 3 = 3. The Greatest Common Factor of 6 and 21 is 3.</p>

26 <p><strong>Step 3:</strong>Multiply the common prime factors. 3 = 3. The Greatest Common Factor of 6 and 21 is 3.</p>

28 <h2>GCF of 6 and 21 Using Division Method or Euclidean Algorithm Method</h2>

27 <h2>GCF of 6 and 21 Using Division Method or Euclidean Algorithm Method</h2>

29 <p>Find the GCF of 6 and 21 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

28 <p>Find the GCF of 6 and 21 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 21 by 6. 21 ÷ 6 = 3 (<a>quotient</a>), The<a>remainder</a>is calculated as 21 - (6×3) = 3. The remainder is 3, not zero, so continue the process.</p>

29 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number. Here, divide 21 by 6. 21 ÷ 6 = 3 (<a>quotient</a>), The<a>remainder</a>is calculated as 21 - (6×3) = 3. The remainder is 3, not zero, so continue the process.</p>

31 <p><strong>Step 2:</strong>Now divide the previous divisor (6) by the previous remainder (3). Divide 6 by 3. 6 ÷ 3 = 2 (quotient), remainder = 6 - (3×2) = 0.</p>

30 <p><strong>Step 2:</strong>Now divide the previous divisor (6) by the previous remainder (3). Divide 6 by 3. 6 ÷ 3 = 2 (quotient), remainder = 6 - (3×2) = 0.</p>

32 <p>The remainder is zero, the divisor will become the GCF. The GCF of 6 and 21 is 3.</p>

31 <p>The remainder is zero, the divisor will become the GCF. The GCF of 6 and 21 is 3.</p>

33 <h2>Common Mistakes and How to Avoid Them in GCF of 6 and 21</h2>

32 <h2>Common Mistakes and How to Avoid Them in GCF of 6 and 21</h2>

34 <p>Finding GCF of 6 and 21 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

33 <p>Finding GCF of 6 and 21 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

35 <h3>Problem 1</h3>

34 <h3>Problem 1</h3>

36 <p>A farmer has 6 apple trees and 21 orange trees. He wants to plant them in rows with the same number of trees in each row. How many trees will be in each row?</p>

35 <p>A farmer has 6 apple trees and 21 orange trees. He wants to plant them in rows with the same number of trees in each row. How many trees will be in each row?</p>

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

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

38 <p>We should find GCF of 6 and 21. GCF of 6 and 21 3.</p>

37 <p>We should find GCF of 6 and 21. GCF of 6 and 21 3.</p>

39 <p>There are 3 equal groups. 6 ÷ 3 = 2</p>

38 <p>There are 3 equal groups. 6 ÷ 3 = 2</p>

40 <p>21 ÷ 3 = 7</p>

39 <p>21 ÷ 3 = 7</p>

41 <p>There will be 3 rows, and each row gets 2 apple trees and 7 orange trees.</p>

40 <p>There will be 3 rows, and each row gets 2 apple trees and 7 orange trees.</p>

42 <h3>Explanation</h3>

41 <h3>Explanation</h3>

43 <p>As the GCF of 6 and 21 is 3, the farmer can make 3 rows. Now divide 6 and 21 by 3. Each row gets 2 apple trees and 7 orange trees.</p>

42 <p>As the GCF of 6 and 21 is 3, the farmer can make 3 rows. Now divide 6 and 21 by 3. Each row gets 2 apple trees and 7 orange trees.</p>

44 <p>Well explained 👍</p>

43 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

44 <h3>Problem 2</h3>

46 <p>A chef has 6 red bowls and 21 blue bowls. He wants to arrange them in stacks with the same number of bowls in each stack, using the largest possible number of bowls per stack. How many bowls will be in each stack?</p>

45 <p>A chef has 6 red bowls and 21 blue bowls. He wants to arrange them in stacks with the same number of bowls in each stack, using the largest possible number of bowls per stack. How many bowls will be in each stack?</p>

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

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

48 <p>GCF of 6 and 21 3. So each stack will have 3 bowls.</p>

47 <p>GCF of 6 and 21 3. So each stack will have 3 bowls.</p>

49 <h3>Explanation</h3>

48 <h3>Explanation</h3>

50 <p>There are 6 red bowls and 21 blue bowls. To find the total number of bowls in each stack, we should find the GCF of 6 and 21. There will be 3 bowls in each stack.</p>

49 <p>There are 6 red bowls and 21 blue bowls. To find the total number of bowls in each stack, we should find the GCF of 6 and 21. There will be 3 bowls in each stack.</p>

51 <p>Well explained 👍</p>

50 <p>Well explained 👍</p>

52 <h3>Problem 3</h3>

51 <h3>Problem 3</h3>

53 <p>A landscaper has 6 meters of red fencing and 21 meters of green fencing. She wants to cut both fences into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

52 <p>A landscaper has 6 meters of red fencing and 21 meters of green fencing. She wants to cut both fences into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

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

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

55 <p>For calculating the longest equal length, we have to calculate the GCF of 6 and 21. The GCF of 6 and 21 3. The fencing is 3 meters long.</p>

54 <p>For calculating the longest equal length, we have to calculate the GCF of 6 and 21. The GCF of 6 and 21 3. The fencing is 3 meters long.</p>

56 <h3>Explanation</h3>

55 <h3>Explanation</h3>

57 <p>For calculating the longest length of the fencing first we need to calculate the GCF of 6 and 21 which is 3. The length of each piece of fencing will be 3 meters.</p>

56 <p>For calculating the longest length of the fencing first we need to calculate the GCF of 6 and 21 which is 3. The length of each piece of fencing will be 3 meters.</p>

58 <p>Well explained 👍</p>

57 <p>Well explained 👍</p>

59 <h3>Problem 4</h3>

58 <h3>Problem 4</h3>

60 <p>A carpenter has two wooden planks, one 6 cm long and the other 21 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>

59 <p>A carpenter has two wooden planks, one 6 cm long and the other 21 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>Okay, lets begin</p>

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

62 <p>The carpenter needs the longest piece of wood. GCF of 6 and 21 3. The longest length of each piece is 3 cm.</p>

61 <p>The carpenter needs the longest piece of wood. GCF of 6 and 21 3. The longest length of each piece is 3 cm.</p>

63 <h3>Explanation</h3>

62 <h3>Explanation</h3>

64 <p>To find the longest length of each piece of the two wooden planks, 6 cm and 21 cm, respectively. We have to find the GCF of 6 and 21, which is 3 cm. The longest length of each piece is 3 cm.</p>

63 <p>To find the longest length of each piece of the two wooden planks, 6 cm and 21 cm, respectively. We have to find the GCF of 6 and 21, which is 3 cm. The longest length of each piece is 3 cm.</p>

65 <p>Well explained 👍</p>

64 <p>Well explained 👍</p>

66 <h3>Problem 5</h3>

65 <h3>Problem 5</h3>

67 <p>If the GCF of 6 and ‘b’ is 3, and the LCM is 42. Find ‘b’.</p>

66 <p>If the GCF of 6 and ‘b’ is 3, and the LCM is 42. Find ‘b’.</p>

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

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

69 <p>The value of ‘b’ is 21.</p>

68 <p>The value of ‘b’ is 21.</p>

70 <h3>Explanation</h3>

69 <h3>Explanation</h3>

71 <p>GCF x LCM = product of the numbers 3 × 42 = 6 × b 126 = 6b b = 126 ÷ 6 = 21</p>

70 <p>GCF x LCM = product of the numbers 3 × 42 = 6 × b 126 = 6b b = 126 ÷ 6 = 21</p>

72 <p>Well explained 👍</p>

71 <p>Well explained 👍</p>

73 <h2>FAQs on the Greatest Common Factor of 6 and 21</h2>

72 <h2>FAQs on the Greatest Common Factor of 6 and 21</h2>

74 <h3>1.What is the LCM of 6 and 21?</h3>

73 <h3>1.What is the LCM of 6 and 21?</h3>

75 <p>The LCM of 6 and 21 is 42.</p>

74 <p>The LCM of 6 and 21 is 42.</p>

76 <h3>2.Is 6 divisible by 2?</h3>

75 <h3>2.Is 6 divisible by 2?</h3>

77 <p>Yes, 6 is divisible by 2 because it is an even number.</p>

76 <p>Yes, 6 is divisible by 2 because it is an even number.</p>

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

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

79 <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>

78 <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>

80 <h3>4.What is the prime factorization of 21?</h3>

79 <h3>4.What is the prime factorization of 21?</h3>

81 <p>The prime factorization of 21 is 3 x 7.</p>

80 <p>The prime factorization of 21 is 3 x 7.</p>

82 <h3>5.Are 6 and 21 prime numbers?</h3>

81 <h3>5.Are 6 and 21 prime numbers?</h3>

83 <p>No, 6 and 21 are not prime numbers because both of them have more than two factors.</p>

82 <p>No, 6 and 21 are not prime numbers because both of them have more than two factors.</p>

84 <h2>Important Glossaries for GCF of 6 and 21</h2>

83 <h2>Important Glossaries for GCF of 6 and 21</h2>

85 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 6 are 1, 2, 3, and 6.</li>

84 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 6 are 1, 2, 3, and 6.</li>

86 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, and so on.</li>

85 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, and so on.</li>

87 </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>

86 </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>

88 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 21 is divided by 6, the remainder is 3 and the quotient is 3.</li>

87 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 21 is divided by 6, the remainder is 3 and the quotient is 3.</li>

89 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 6 and 21 is 3, as it is their largest common factor that divides the numbers completely.</li>

88 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 6 and 21 is 3, as it is their largest common factor that divides the numbers completely.</li>

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

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

91 <p>▶</p>

90 <p>▶</p>

92 <h2>Hiralee Lalitkumar Makwana</h2>

91 <h2>Hiralee Lalitkumar Makwana</h2>

93 <h3>About the Author</h3>

92 <h3>About the Author</h3>

94 <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>

93 <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>

95 <h3>Fun Fact</h3>

94 <h3>Fun Fact</h3>

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

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