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2 <p>Last updated on<strong>October 3, 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 10 and 21.</p>

4 <h2>What is the GCF of 10 and 21?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>10 and 21 is 1.</p>

6 <p>The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the numbers.</p>

7 <p>If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.</p>

8 <p>The GCF of two numbers cannot be negative because divisors are always positive.</p>

9 <h2>How to find the GCF of 10 and 21?</h2>

10 <p>To find the GCF of 10 and 21, a few methods are described below -</p>

11 <p>Listing Factors Prime Factorization Long Division Method / Euclidean Algorithm</p>

12 <h2>GCF of 10 and 21 by Using Listing of factors</h2>

13 <p>Steps to find the GCF of 10 and 21 using the listing of<a>factors</a></p>

14 <p>Step 1: Firstly, list the factors of each number Factors of 10 = 1, 2, 5, 10. Factors of 21 = 1, 3, 7, 21.</p>

15 <p>Step 2: Now, identify the<a>common factors</a>of them Common factor of 10 and 21: 1.</p>

16 <p>Step 3: Choose the largest factor, The largest factor that both numbers have is 1.</p>

17 <p>The GCF of 10 and 21 is 1.</p>

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20 <h2>GCF of 10 and 21 Using Prime Factorization</h2>

19 <h2>GCF of 10 and 21 Using Prime Factorization</h2>

21 <p>To find the GCF of 10 and 21 using the Prime Factorization Method, follow these steps:</p>

20 <p>To find the GCF of 10 and 21 using the Prime Factorization Method, follow these steps:</p>

22 <p>Step 1: Find the<a>prime factors</a>of each number Prime Factors of 10: 10 = 2 x 5 Prime Factors of 21: 21 = 3 x 7</p>

21 <p>Step 1: Find the<a>prime factors</a>of each number Prime Factors of 10: 10 = 2 x 5 Prime Factors of 21: 21 = 3 x 7</p>

23 <p>Step 2: Now, identify the common prime factors There are no common prime factors.</p>

22 <p>Step 2: Now, identify the common prime factors There are no common prime factors.</p>

24 <p>Step 3: Since there are no common prime factors, the GCF is 1.</p>

23 <p>Step 3: Since there are no common prime factors, the GCF is 1.</p>

25 <p>The Greatest Common Factor of 10 and 21 is 1.</p>

24 <p>The Greatest Common Factor of 10 and 21 is 1.</p>

26 <h2>GCF of 10 and 21 Using Division Method or Euclidean Algorithm</h2>

25 <h2>GCF of 10 and 21 Using Division Method or Euclidean Algorithm</h2>

27 <p>Find the GCF of 10 and 21 using the<a>division</a>method or Euclidean Algorithm.</p>

26 <p>Find the GCF of 10 and 21 using the<a>division</a>method or Euclidean Algorithm.</p>

28 <p>Follow these steps:</p>

27 <p>Follow these steps:</p>

29 <p>Step 1: First, divide the larger number by the smaller number Here, divide 21 by 10 21 ÷ 10 = 2 (<a>quotient</a>), The<a>remainder</a>is calculated as 21 - (10×2) = 1 The remainder is 1, not zero, so continue the process.</p>

28 <p>Step 1: First, divide the larger number by the smaller number Here, divide 21 by 10 21 ÷ 10 = 2 (<a>quotient</a>), The<a>remainder</a>is calculated as 21 - (10×2) = 1 The remainder is 1, not zero, so continue the process.</p>

30 <p>Step 2: Now divide the previous divisor (10) by the previous remainder (1) Divide 10 by 1 10 ÷ 1 = 10 (quotient), remainder = 10 - (1×10) = 0, The remainder is zero, the divisor will become the GCF.</p>

29 <p>Step 2: Now divide the previous divisor (10) by the previous remainder (1) Divide 10 by 1 10 ÷ 1 = 10 (quotient), remainder = 10 - (1×10) = 0, The remainder is zero, the divisor will become the GCF.</p>

31 <p>The GCF of 10 and 21 is 1.</p>

30 <p>The GCF of 10 and 21 is 1.</p>

32 <h2>Common Mistakes and How to Avoid Them in GCF of 10 and 21</h2>

31 <h2>Common Mistakes and How to Avoid Them in GCF of 10 and 21</h2>

33 <p>Finding the GCF of 10 and 21 seems simple, but students often make mistakes while calculating the GCF.</p>

32 <p>Finding the GCF of 10 and 21 seems simple, but students often make mistakes while calculating the GCF.</p>

34 <p>Here are some common mistakes to be avoided by the students.</p>

33 <p>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 teacher has 10 apples and 21 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>

35 <p>A teacher has 10 apples and 21 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>

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

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

38 <p>We should find the GCF of 10 and 21. GCF of 10 and 21 is 1.</p>

37 <p>We should find the GCF of 10 and 21. GCF of 10 and 21 is 1.</p>

39 <p>There are 1 equal groups. 10 ÷ 1 = 10 21 ÷ 1 = 21.</p>

38 <p>There are 1 equal groups. 10 ÷ 1 = 10 21 ÷ 1 = 21.</p>

40 <p>There will be 1 group, and each group gets 10 apples and 21 oranges.</p>

39 <p>There will be 1 group, and each group gets 10 apples and 21 oranges.</p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>As the GCF of 10 and 21 is 1, the teacher can make 1 group. Now divide 10 and 21 by 1.</p>

41 <p>As the GCF of 10 and 21 is 1, the teacher can make 1 group. Now divide 10 and 21 by 1.</p>

43 <p>Each group gets 10 apples and 21 oranges.</p>

42 <p>Each group gets 10 apples and 21 oranges.</p>

44 <p>Well explained 👍</p>

43 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

44 <h3>Problem 2</h3>

46 <p>A school has 10 red chairs and 21 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?</p>

45 <p>A school has 10 red chairs and 21 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?</p>

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

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

48 <p>GCF of 10 and 21 is 1.</p>

47 <p>GCF of 10 and 21 is 1.</p>

49 <p>So each row will have 1 chair.</p>

48 <p>So each row will have 1 chair.</p>

50 <h3>Explanation</h3>

49 <h3>Explanation</h3>

51 <p>There are 10 red and 21 blue chairs.</p>

50 <p>There are 10 red and 21 blue chairs.</p>

52 <p>To find the total number of chairs in each row, we should find the GCF of 10 and 21.</p>

51 <p>To find the total number of chairs in each row, we should find the GCF of 10 and 21.</p>

53 <p>There will be 1 chair in each row.</p>

52 <p>There will be 1 chair in each row.</p>

54 <p>Well explained 👍</p>

53 <p>Well explained 👍</p>

55 <h3>Problem 3</h3>

54 <h3>Problem 3</h3>

56 <p>A tailor has 10 meters of red ribbon and 21 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

55 <p>A tailor has 10 meters of red ribbon and 21 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>

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

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

58 <p>For calculating the longest equal length, we have to calculate the GCF of 10 and 21.</p>

57 <p>For calculating the longest equal length, we have to calculate the GCF of 10 and 21.</p>

59 <p>The GCF of 10 and 21 is 1.</p>

58 <p>The GCF of 10 and 21 is 1.</p>

60 <p>The ribbon is 1 meter long.</p>

59 <p>The ribbon is 1 meter long.</p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>For calculating the longest length of the ribbon, first we need to calculate the GCF of 10 and 21, which is 1.</p>

61 <p>For calculating the longest length of the ribbon, first we need to calculate the GCF of 10 and 21, which is 1.</p>

63 <p>The length of each piece of the ribbon will be 1 meter.</p>

62 <p>The length of each piece of the ribbon will be 1 meter.</p>

64 <p>Well explained 👍</p>

63 <p>Well explained 👍</p>

65 <h3>Problem 4</h3>

64 <h3>Problem 4</h3>

66 <p>A carpenter has two wooden planks, one 10 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>

65 <p>A carpenter has two wooden planks, one 10 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>

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

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

68 <p>The carpenter needs the longest piece of wood. GCF of 10 and 21 is 1.</p>

67 <p>The carpenter needs the longest piece of wood. GCF of 10 and 21 is 1.</p>

69 <p>The longest length of each piece is 1 cm.</p>

68 <p>The longest length of each piece is 1 cm.</p>

70 <h3>Explanation</h3>

69 <h3>Explanation</h3>

71 <p>To find the longest length of each piece of the two wooden planks, 10 cm and 21 cm, respectively, we have to find the GCF of 10 and 21, which is 1 cm.</p>

70 <p>To find the longest length of each piece of the two wooden planks, 10 cm and 21 cm, respectively, we have to find the GCF of 10 and 21, which is 1 cm.</p>

72 <p>The longest length of each piece is 1 cm.</p>

71 <p>The longest length of each piece is 1 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 10 and ‘a’ is 1, and the LCM is 210. Find ‘a’.</p>

74 <p>If the GCF of 10 and ‘a’ is 1, and the LCM is 210. Find ‘a’.</p>

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

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

77 <p>The value of ‘a’ is 21.</p>

76 <p>The value of ‘a’ is 21.</p>

78 <h3>Explanation</h3>

77 <h3>Explanation</h3>

79 <p>GCF x LCM = product of the numbers 1 × 210 = 10 × a 210 = 10a a = 210 ÷ 10 = 21</p>

78 <p>GCF x LCM = product of the numbers 1 × 210 = 10 × a 210 = 10a a = 210 ÷ 10 = 21</p>

80 <p>Well explained 👍</p>

79 <p>Well explained 👍</p>

81 <h2>FAQs on the Greatest Common Factor of 10 and 21</h2>

80 <h2>FAQs on the Greatest Common Factor of 10 and 21</h2>

82 <h3>1.What is the LCM of 10 and 21?</h3>

81 <h3>1.What is the LCM of 10 and 21?</h3>

83 <p>The LCM of 10 and 21 is 210.</p>

82 <p>The LCM of 10 and 21 is 210.</p>

84 <h3>2.Is 10 divisible by 2?</h3>

83 <h3>2.Is 10 divisible by 2?</h3>

85 <p>Yes, 10 is divisible by 2 because it is an even number.</p>

84 <p>Yes, 10 is divisible by 2 because it is an even number.</p>

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

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

87 <p>The common factor of<a>prime numbers</a>is 1 and the number itself.</p>

86 <p>The common factor of<a>prime numbers</a>is 1 and the number itself.</p>

88 <p>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>

87 <p>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>

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

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

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

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

91 <h3>5.Are 10 and 21 prime numbers?</h3>

90 <h3>5.Are 10 and 21 prime numbers?</h3>

92 <p>No, 10 and 21 are not prime numbers because both of them have more than two factors.</p>

91 <p>No, 10 and 21 are not prime numbers because both of them have more than two factors.</p>

93 <h2>Important Glossaries for GCF of 10 and 21</h2>

92 <h2>Important Glossaries for GCF of 10 and 21</h2>

94 <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>

93 <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>

95 </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>

94 </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>

96 </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>

95 </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>

97 </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 10, the remainder is 1 and the quotient is 2.</li>

96 </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 10, the remainder is 1 and the quotient is 2.</li>

98 </ul><ul><li><strong>LCM</strong>: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 10 and 21 is 210.</li>

97 </ul><ul><li><strong>LCM</strong>: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 10 and 21 is 210.</li>

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

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

100 <p>▶</p>

99 <p>▶</p>

101 <h2>Hiralee Lalitkumar Makwana</h2>

100 <h2>Hiralee Lalitkumar Makwana</h2>

102 <h3>About the Author</h3>

101 <h3>About the Author</h3>

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>

102 <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>

104 <h3>Fun Fact</h3>

103 <h3>Fun Fact</h3>

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

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