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2 <p>Last updated on<strong>December 17, 2025</strong></p>

3 <p>Numbers whose dividend is completely divisible by quotient are its factors. In real life, factors are helpful in scenarios like packing boxes and arranging seats. In this article, we will be studying examples, mistakes, and methods to solve factors of 21.</p>

4 <h2>What are the Factors of 21</h2>

5 <p>The<a>factors</a><a>of</a>21 are 1, 3, 7 and 21</p>

6 <p><strong>Negative Factors-</strong>These are negative counterparts of the positive factors.</p>

7 <p>Negative factors: -1, -3, -7, -21</p>

8 <p><strong>Prime Factors -</strong>Prime factors are the<a>prime numbers</a>themselves, when multiplied together, give 21 as the<a>product</a>. Prime factor: 3, 7 </p>

9 <p><strong>Prime Factorization-</strong>Prime factorization involves breaking 21 into its<a>prime factors</a></p>

10 <p>It is expressed as 31 × 71</p>

11 <p>The factors of<strong>21</strong>can be written as shown in the table given below:</p>

12 <strong>Factor</strong><strong>Type Values</strong>Positive Factors of 21 1, 3, 7, 21 Negative Factors of 21 -1, -3, -7, -21 Prime Factors of 21 3, 7 Prime Factorization of 21 3 × 7 The Sum of the Factors of 21 32<h2>How to Find the Factors of 21</h2>

13 <p>There are different methods to find the factors of 21.</p>

14 <p>Methods to find the factors of 21:</p>

15 <ul><li>Multiplication Method</li>

16 </ul><ul><li>Division Method</li>

17 </ul><ul><li>Prime Factor and Prime Factorization</li>

18 </ul><h3>Finding Factors Using Multiplication Method</h3>

19 <p>The<a>multiplication</a>method finds the pair of factors that give 21 as their product.</p>

20 <p>Step-by-step process</p>

21 <p><strong>Step 1:</strong>Find the pair of<a>numbers</a>whose product is 21. </p>

22 <p><strong>Step 2:</strong>The factors are those numbers, when multiplied, give 21.</p>

23 <p><strong>Step 3:</strong>Make a list of numbers whose product will be 21.</p>

24 <p>A list of numbers whose products are 21 is given below:</p>

25 <p>1 × 21 = 21</p>

26 <p>3 × 7 = 21 </p>

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29 <h3>Finding Factors Using Division Method</h3>

28 <h3>Finding Factors Using Division Method</h3>

30 <p>The<a>division</a>method finds the numbers that fully divide the given number. </p>

29 <p>The<a>division</a>method finds the numbers that fully divide the given number. </p>

31 <p>Step-by-step process</p>

30 <p>Step-by-step process</p>

32 <p><strong>Step 1:</strong>Since every number is divisible by 1, 1 will always be a factor. Example: 21÷1 = 21</p>

31 <p><strong>Step 1:</strong>Since every number is divisible by 1, 1 will always be a factor. Example: 21÷1 = 21</p>

33 <p><strong>Step 2:</strong>Move to the next<a>integer</a>. Both<a>divisor</a>and<a>quotient</a>are the factors. </p>

32 <p><strong>Step 2:</strong>Move to the next<a>integer</a>. Both<a>divisor</a>and<a>quotient</a>are the factors. </p>

34 <p>Overview of Factors of 21 using the division method</p>

33 <p>Overview of Factors of 21 using the division method</p>

35 <h2>Prime Factors and Prime Factorization</h2>

34 <h2>Prime Factors and Prime Factorization</h2>

36 <h3>Prime Factors of 21</h3>

35 <h3>Prime Factors of 21</h3>

37 <p>Prime Factors of 21-There is only one prime factor for 21</p>

36 <p>Prime Factors of 21-There is only one prime factor for 21</p>

38 <p>Prime factors of 21: 3, 7</p>

37 <p>Prime factors of 21: 3, 7</p>

39 <p>Steps to find the prime factors of 21</p>

38 <p>Steps to find the prime factors of 21</p>

40 <p><strong>Step 1:</strong> Divide 21 using the prime number 3</p>

39 <p><strong>Step 1:</strong> Divide 21 using the prime number 3</p>

41 <p>21÷3 = 7</p>

40 <p>21÷3 = 7</p>

42 <p><strong>Step 2:</strong>Divide 5 with the prime number 7</p>

41 <p><strong>Step 2:</strong>Divide 5 with the prime number 7</p>

43 <p>7÷7 = 1</p>

42 <p>7÷7 = 1</p>

44 <h3>Prime Factorization of 21</h3>

43 <h3>Prime Factorization of 21</h3>

45 <p><strong>Prime Factorization of 21-</strong>Prime Factorization breaks down the prime factors of 21</p>

44 <p><strong>Prime Factorization of 21-</strong>Prime Factorization breaks down the prime factors of 21</p>

46 <p>Expressed as 31 × 71</p>

45 <p>Expressed as 31 × 71</p>

47 <h4><strong>Factor Tree</strong></h4>

46 <h4><strong>Factor Tree</strong></h4>

48 <p>The prime factorization is visually represented using the<a>factor tree</a>. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.</p>

47 <p>The prime factorization is visually represented using the<a>factor tree</a>. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.</p>

49 <p><strong>Factor Tree for 21:</strong></p>

48 <p><strong>Factor Tree for 21:</strong></p>

50 <h2>Factor Pairs of 21</h2>

49 <h2>Factor Pairs of 21</h2>

51 <p>The factors of<strong>21</strong>can be written in both positive and negative pairs. The table below represents the factor pairs of<strong>21</strong>, where the product of each pair of numbers is equal to<strong>21</strong>.</p>

50 <p>The factors of<strong>21</strong>can be written in both positive and negative pairs. The table below represents the factor pairs of<strong>21</strong>, where the product of each pair of numbers is equal to<strong>21</strong>.</p>

52 <p><strong>Positive Pair Factors of 21:</strong></p>

51 <p><strong>Positive Pair Factors of 21:</strong></p>

53 <strong>Factors</strong><strong>Positive Pair Factors</strong>1 × 21 = 21 1, 21 3 × 7 = 21 3, 7<p>Since the product of two negative numbers is also positive,<strong>21</strong>also has negative pair factors.</p>

52 <strong>Factors</strong><strong>Positive Pair Factors</strong>1 × 21 = 21 1, 21 3 × 7 = 21 3, 7<p>Since the product of two negative numbers is also positive,<strong>21</strong>also has negative pair factors.</p>

54 <p><strong>Negative Pair Factors of 21:</strong></p>

53 <p><strong>Negative Pair Factors of 21:</strong></p>

55 <strong>Factors</strong><strong>Negative Pair Factors</strong>-1 × -21 = 21 -1, -21 -3 × -7 = 21 -3, -7<h2>Common Mistakes and How to Avoid Them in Factors of 21</h2>

54 <strong>Factors</strong><strong>Negative Pair Factors</strong>-1 × -21 = 21 -1, -21 -3 × -7 = 21 -3, -7<h2>Common Mistakes and How to Avoid Them in Factors of 21</h2>

56 <p>Mistakes can occur while finding the factors. Learn about the common errors that can occur. Solutions to solve the common mistakes are given below. </p>

55 <p>Mistakes can occur while finding the factors. Learn about the common errors that can occur. Solutions to solve the common mistakes are given below. </p>

56 + <h2>Download Worksheets</h2>

57 <h3>Problem 1</h3>

58 <p>Can you express 21 as a product of two factors other than 1 and 21?</p>

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

60 <p>Yes, 21 can be expressed as a product of factors 3 and 7. </p>

61 <h3>Explanation</h3>

62 <p>When 3 is multiplied by 7 (3×7) we get 21 as the product. Other than the factors 1 and 21, we can also multiply 3 and 7 to get the product 21. </p>

63 <p>Well explained 👍</p>

64 <h3>Problem 2</h3>

65 <p>What is the sum of factors of 21?</p>

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

67 <p>The sum of factors of 21 is 32 </p>

68 <h3>Explanation</h3>

69 <p>Write the factors of 21 and add them together to get the sum.</p>

70 <p>The factors of 21 are 1, 3, 7 and 21. Sum of factors = 1+3+7+21 = 32</p>

71 <p>Well explained 👍</p>

72 <h3>Problem 3</h3>

73 <p>Identify the factor pair whose sum is 10</p>

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

75 <p>The factor pair is (3,7) </p>

76 <h3>Explanation</h3>

77 <p>When the factor pair (3,7) is added (3 + 7), we get 10 as the sum. </p>

78 <p>Well explained 👍</p>

79 <h3>Problem 4</h3>

80 <p>At a Costco store in Chicago, a teacher buys 21 snack packs for a school event. She wants to arrange the packs equally into rows with no leftovers. What are all the possible numbers of packs she can place in each row?</p>

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

82 <p>1, 3, 7, 21</p>

83 <h3>Explanation</h3>

84 <p>To arrange the snack packs evenly, we find all the factors of 21. Factors are numbers that divide 21 exactly without leaving a remainder.</p>

85 <p>21 ÷ 1 = 21 21 ÷ 3 = 7 21 ÷ 7 = 3 21 ÷ 21 = 1</p>

86 <p>So, the factors of 21 are 1, 3, 7, and 21.</p>

87 <p>Well explained 👍</p>

88 <h3>Problem 5</h3>

89 <p>A youth NFL football camp in Dallas orders 21 jerseys for players. The coach wants to divide the jerseys equally among groups. Which group sizes are possible without any jersey left over?</p>

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

91 <p>1, 3, 7, 21</p>

92 <h3>Explanation</h3>

93 <p>To divide the jerseys equally, the group size must be a factor of 21.</p>

94 <p>Since 21 can be divided evenly by 1, 3, 7, and 21, these are the possible group sizes. Any other number would leave leftover jerseys.</p>

95 <p>Well explained 👍</p>

96 <h3>Problem 6</h3>

97 <p>A CVS pharmacy in Boston receives a shipment of 21 medicine sample packets for a school science health program. The packets must be divided equally among students. What are the possible numbers of students who can receive the packets evenly?</p>

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

99 <p>1, 3, 7, 21</p>

100 <h3>Explanation</h3>

101 <p>To distribute the medicine packets evenly, we list the factors of 21.</p>

102 <p>Only numbers that divide 21 completely are valid. These are 1, 3, 7, and 21.</p>

103 <p>So, the packets can be shared evenly among 1, 3, 7, or 21 students.</p>

104 <p>Well explained 👍</p>

105 <h2>FAQs on Factors of 21</h2>

106 <h3>1.Does 21 only have 2 factors?</h3>

107 <p>No, there are 4 factors of 21. The factors of 21 are 1, 3, 7 and 21. </p>

108 <h3>2.Is 21 a prime factor?</h3>

109 <p>No, 21 is not a prime factor because it has more than two factors. Any number with more than two factors are composite. Hence, 21 is a<a>composite number</a>. The factors of 21 are 1, 3, 7 and 21. </p>

110 <h3>3.What is the factor tree of 21?</h3>

111 <p>A factor tree of 21 visually represents its prime factors as branches of the tree. The prime factors of 21 are 3 and 7. </p>

112 <h3>4.Is 18 a factor of 21?</h3>

113 <p>No, 18 is not a factor of 21 because 21 can't be completely divided by 18. When 21 is divided by 18, the<a>remainder</a>is not zero. Factors are numbers that can divide 21 completely. </p>

114 <h3>5.Is 21 a factor of 28?</h3>

115 <p>No, 21 is not a factor of 28 because 28 can't be completely divided by 21. When 28 is divided by 21, the remainder is not zero. Factors are numbers that can divide 28 completely. </p>

116 <h3>6.How many factors does 21 have?</h3>

117 <p>The number<strong>21 has 4 factors</strong>. Factors are whole numbers that divide 21 evenly without leaving a remainder. These factors come in pairs that multiply to give 21.</p>

118 <h3>7.What is the smallest factor of 21?</h3>

119 <p>The<strong>smallest factor of 21</strong>is<strong>1</strong>. This is because 1 divides every whole number evenly and is always the smallest possible factor.</p>

120 <h3>8.What is the largest factor of 21?</h3>

121 <p>The<strong>highest factor of 21</strong>is<strong>21</strong>itself. Every number is divisible by itself, so the largest factor of a number is always the number itself.</p>

122 <h3>9.Which factors of 21 add up to 13?</h3>

123 <p>The factors of 21 that add up to<strong>13</strong>are<strong>3 and 10</strong>. These two numbers add to 13, but<strong>10 is not a factor of 21</strong>, so<strong>there are no factors of 21 that add up to 13</strong>.</p>

124 <h3>10.How many even factors does 21 have?</h3>

125 <p>The number<strong>21 has 0 even factors</strong>. This is because 21 is an odd number and is not divisible by 2, so none of its factors are even.</p>

126 <h3>11.What are the odd factors of 21?</h3>

127 <p>The<strong>odd factors of 21</strong>are<strong>1, 3, 7, and 21</strong>. All the factors of an odd number are odd.</p>

128 <h3>12.What is the sum of all the factors of 21?</h3>

129 <p>The<strong>sum of all the factors of 21 is 32</strong>.</p>

130 <p>Adding all the factors together gives: 1 + 3 + 7 + 21 = 32.</p>

131 <h2>Hiralee Lalitkumar Makwana</h2>

132 <h3>About the Author</h3>

133 <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>

134 <h3>Fun Fact</h3>

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