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1 - <p>291 Learners</p>

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2 <p>Last updated on<strong>December 12, 2025</strong></p>

3 <p>Factors are numbers that divide a given number evenly without a remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of -81, how they are used in real life, and tips to learn them quickly.</p>

4 <h2>What are the Factors of -81?</h2>

5 <p>The<a>numbers</a>that divide -81 evenly are known as<a>factors</a>of -81.</p>

6 <p>A factor of -81 is a number that divides the number without leaving a<a>remainder</a>.</p>

7 <p>The Positive factors of -81 are 1, 3, 9, 27, 81,</p>

8 <p><strong>The negative factors of -81:</strong>-1, -3, -9, -27, -81.</p>

9 <p><strong>Prime factors of -81:</strong>3.</p>

10 <p><strong>Prime factorization of -81:</strong>34.</p>

11 <p>The<a>sum</a>of factors of 81 (ignoring the negative factors): 1 + 3 + 9 + 27 + 81 = 121.</p>

12 <h2>How to Find Factors of -81?</h2>

13 <p>Factors can be found using different methods. Mentioned below are some commonly used methods:</p>

14 <ul><li>Finding factors using<a>multiplication</a> </li>

15 <li>Finding factors using the<a>division</a>method </li>

16 <li>Prime factors and<a>prime factorization</a></li>

17 </ul><h3>Finding Factors Using Multiplication</h3>

18 <p>To find factors using multiplication, we need to identify pairs of numbers that multiply to give -81. Identifying the numbers which are multiplied to get -81 is the multiplication method.</p>

19 <p><strong>Step 1:</strong>Multiply -81 by 1, -81 × 1 = -81.</p>

20 <p><strong>Step 2:</strong>Check for other numbers that give -81when multiplied:</p>

21 <p>3 × -27 = -81</p>

22 <p>9 × -9 = -81</p>

23 <p>27 × -3 = -81</p>

24 <p>81 × -1 = -81</p>

25 <p>Therefore, the factor pairs of -81 are: (1, -81), (3, -27), (9, -9), (-1, 81), (-3, 27), (-9, 9).</p>

26 <p>For every positive factor, there is a negative factor.</p>

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

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

30 <p>Divide the given number by<a>whole numbers</a>until the remainder becomes zero, and list out the numbers which result in whole numbers as factors. Factors can be calculated using the division method:</p>

29 <p>Divide the given number by<a>whole numbers</a>until the remainder becomes zero, and list out the numbers which result in whole numbers as factors. Factors can be calculated using the division method:</p>

31 <p><strong>Step 1:</strong>Divide -81 by -1, -81 ÷ -1 = 81.</p>

30 <p><strong>Step 1:</strong>Divide -81 by -1, -81 ÷ -1 = 81.</p>

32 <p><strong>Step 2:</strong>Continue dividing -81 by numbers until the remainder becomes 0.</p>

31 <p><strong>Step 2:</strong>Continue dividing -81 by numbers until the remainder becomes 0.</p>

33 <p>-81 ÷ 1 = -81</p>

32 <p>-81 ÷ 1 = -81</p>

34 <p>-81 ÷ 3 = -27</p>

33 <p>-81 ÷ 3 = -27</p>

35 <p>-81 ÷ 9 = -9</p>

34 <p>-81 ÷ 9 = -9</p>

36 <p>-81 ÷ 27 = -3</p>

35 <p>-81 ÷ 27 = -3</p>

37 <p>-81 ÷ 81 = -1</p>

36 <p>-81 ÷ 81 = -1</p>

38 <p>Therefore, the factors of -81 are: 1, 3, 9, 27, 81, -1, -3, -9, -27, -81.</p>

37 <p>Therefore, the factors of -81 are: 1, 3, 9, 27, 81, -1, -3, -9, -27, -81.</p>

39 <h3>Prime Factors and Prime Factorization</h3>

38 <h3>Prime Factors and Prime Factorization</h3>

40 <p>Factors can be found by dividing the number by<a>prime numbers</a>. We can find the prime factors using the following methods:</p>

39 <p>Factors can be found by dividing the number by<a>prime numbers</a>. We can find the prime factors using the following methods:</p>

41 <ul><li>Using prime factorization</li>

40 <ul><li>Using prime factorization</li>

42 <li>Using a<a>factor tree</a></li>

41 <li>Using a<a>factor tree</a></li>

43 </ul><p><strong>Using Prime Factorization:</strong>In this process, prime factors of -81 divide the number to break it down into the multiplication form of prime factors until the remainder becomes 1.</p>

42 </ul><p><strong>Using Prime Factorization:</strong>In this process, prime factors of -81 divide the number to break it down into the multiplication form of prime factors until the remainder becomes 1.</p>

44 <p>81 ÷ 3 = 27</p>

43 <p>81 ÷ 3 = 27</p>

45 <p>27 ÷ 3 = 9</p>

44 <p>27 ÷ 3 = 9</p>

46 <p>9 ÷ 3 = 3</p>

45 <p>9 ÷ 3 = 3</p>

47 <p>3 ÷ 3 = 1</p>

46 <p>3 ÷ 3 = 1</p>

48 <p>The prime factorization of 81 is:<a>3^4</a>. Thus, the prime factors of -81 are 3.</p>

47 <p>The prime factorization of 81 is:<a>3^4</a>. Thus, the prime factors of -81 are 3.</p>

49 <h3>Factor Tree</h3>

48 <h3>Factor Tree</h3>

50 <p>The factor tree is a graphical representation of breaking down a number into prime factors. The following steps show:</p>

49 <p>The factor tree is a graphical representation of breaking down a number into prime factors. The following steps show:</p>

51 <p><strong>Step 1:</strong>Firstly, divide 81 by 3 to get 27.</p>

50 <p><strong>Step 1:</strong>Firstly, divide 81 by 3 to get 27.</p>

52 <p><strong>Step 2:</strong>Now divide 27 by 3 to get 9.</p>

51 <p><strong>Step 2:</strong>Now divide 27 by 3 to get 9.</p>

53 <p><strong>Step 3:</strong>Then divide 9 by 3 to get 3.</p>

52 <p><strong>Step 3:</strong>Then divide 9 by 3 to get 3.</p>

54 <p><strong>Step 4:</strong>Divide 3 by 3 to get 1.</p>

53 <p><strong>Step 4:</strong>Divide 3 by 3 to get 1.</p>

55 <p>So, the prime factorization of -81 is: 3^4.</p>

54 <p>So, the prime factorization of -81 is: 3^4.</p>

56 <p><strong>Factor Pairs:</strong>Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.</p>

55 <p><strong>Factor Pairs:</strong>Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.</p>

57 <p>Positive factor pairs of -81: (1, -81), (3, -27), (9, -9).</p>

56 <p>Positive factor pairs of -81: (1, -81), (3, -27), (9, -9).</p>

58 <p>Negative factor pairs of -81: (-1, 81), (-3, 27), (-9, 9).</p>

57 <p>Negative factor pairs of -81: (-1, 81), (-3, 27), (-9, 9).</p>

59 <h2>Common Mistakes and How to Avoid Them in Factors of -81</h2>

58 <h2>Common Mistakes and How to Avoid Them in Factors of -81</h2>

60 <p>Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.</p>

59 <p>Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.</p>

61 <h3>Problem 1</h3>

60 <h3>Problem 1</h3>

62 <p>There are 9 players and -81 points to distribute. How will they divide the points equally?</p>

61 <p>There are 9 players and -81 points to distribute. How will they divide the points equally?</p>

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

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

64 <p>They will get -9 points each.</p>

63 <p>They will get -9 points each.</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

66 <p>To divide the points equally, divide the total points by the number of players.</p>

65 <p>To divide the points equally, divide the total points by the number of players.</p>

67 <p>-81/9 = -9</p>

66 <p>-81/9 = -9</p>

68 <p>Well explained 👍</p>

67 <p>Well explained 👍</p>

69 <h3>Problem 2</h3>

68 <h3>Problem 2</h3>

70 <p>A garden is rectangular, with the length of the garden being 27 meters and the total area being -81 square meters. Find the width.</p>

69 <p>A garden is rectangular, with the length of the garden being 27 meters and the total area being -81 square meters. Find the width.</p>

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

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

72 <p>-3 meters.</p>

71 <p>-3 meters.</p>

73 <h3>Explanation</h3>

72 <h3>Explanation</h3>

74 <p>To find the width of the garden, use the formula: Area = length × width -81 = 27 × width</p>

73 <p>To find the width of the garden, use the formula: Area = length × width -81 = 27 × width</p>

75 <p>To find the value of width, shift 27 to the left side.</p>

74 <p>To find the value of width, shift 27 to the left side.</p>

76 <p>-81/27 = width</p>

75 <p>-81/27 = width</p>

77 <p>Width = -3.</p>

76 <p>Width = -3.</p>

78 <p>Well explained 👍</p>

77 <p>Well explained 👍</p>

79 <h3>Problem 3</h3>

78 <h3>Problem 3</h3>

80 <p>A warehouse has 27 crates and -81 items. How many items will be in each crate?</p>

79 <p>A warehouse has 27 crates and -81 items. How many items will be in each crate?</p>

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

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

82 <p>Each crate will have -3 items.</p>

81 <p>Each crate will have -3 items.</p>

83 <h3>Explanation</h3>

82 <h3>Explanation</h3>

84 <p>To find the items in each crate, divide the total items by the crates.</p>

83 <p>To find the items in each crate, divide the total items by the crates.</p>

85 <p>-81/27 = -3</p>

84 <p>-81/27 = -3</p>

86 <p>Well explained 👍</p>

85 <p>Well explained 👍</p>

87 <h3>Problem 4</h3>

86 <h3>Problem 4</h3>

88 <p>In a school, there are -81 students and 3 groups. How many students are there in each group?</p>

87 <p>In a school, there are -81 students and 3 groups. How many students are there in each group?</p>

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

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

90 <p>There are -27 students in each group.</p>

89 <p>There are -27 students in each group.</p>

91 <h3>Explanation</h3>

90 <h3>Explanation</h3>

92 <p>Dividing the students by the total groups, we get the number of students in each group.</p>

91 <p>Dividing the students by the total groups, we get the number of students in each group.</p>

93 <p>-81/3 = -27</p>

92 <p>-81/3 = -27</p>

94 <p>Well explained 👍</p>

93 <p>Well explained 👍</p>

95 <h3>Problem 5</h3>

94 <h3>Problem 5</h3>

96 <p>81 books need to be arranged on 9 shelves. How many books will go on each shelf?</p>

95 <p>81 books need to be arranged on 9 shelves. How many books will go on each shelf?</p>

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

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

98 <p>Each of the shelves has 9 books.</p>

97 <p>Each of the shelves has 9 books.</p>

99 <h3>Explanation</h3>

98 <h3>Explanation</h3>

100 <p>Divide the total books by the number of shelves.</p>

99 <p>Divide the total books by the number of shelves.</p>

101 <p>81/9 = 9</p>

100 <p>81/9 = 9</p>

102 <p>Well explained 👍</p>

101 <p>Well explained 👍</p>

103 <h2>FAQs on Factors of -81</h2>

102 <h2>FAQs on Factors of -81</h2>

104 <h3>1.What are the factors of -81?</h3>

103 <h3>1.What are the factors of -81?</h3>

105 <p>The factors of -81 are 1, 3, 9, 27, 81, -1, -3, -9, -27, -81.</p>

104 <p>The factors of -81 are 1, 3, 9, 27, 81, -1, -3, -9, -27, -81.</p>

106 <h3>2.Mention the prime factors of -81.</h3>

105 <h3>2.Mention the prime factors of -81.</h3>

107 <p>The prime factors of -81 are 3.</p>

106 <p>The prime factors of -81 are 3.</p>

108 <h3>3.Is -81 a multiple of 9?</h3>

107 <h3>3.Is -81 a multiple of 9?</h3>

109 <h3>4.Mention the factor pairs of -81.</h3>

108 <h3>4.Mention the factor pairs of -81.</h3>

110 <p>(1, -81), (3, -27), (9, -9), (-1, 81), (-3, 27), (-9, 9) are the factor pairs of -81.</p>

109 <p>(1, -81), (3, -27), (9, -9), (-1, 81), (-3, 27), (-9, 9) are the factor pairs of -81.</p>

111 <h3>5.What is the square of -81?</h3>

110 <h3>5.What is the square of -81?</h3>

112 <h2>Important Glossaries for Factors of -81</h2>

111 <h2>Important Glossaries for Factors of -81</h2>

113 <ul><li><strong>Factors:</strong>Numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -81 are 1, 3, 9, 27, 81, and their negative counterparts.</li>

112 <ul><li><strong>Factors:</strong>Numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -81 are 1, 3, 9, 27, 81, and their negative counterparts.</li>

114 </ul><ul><li><strong>Prime factors:</strong>Factors that are prime numbers. For example, 3 is a prime factor of -81.</li>

113 </ul><ul><li><strong>Prime factors:</strong>Factors that are prime numbers. For example, 3 is a prime factor of -81.</li>

115 </ul><ul><li><strong>Factor pairs:</strong>Two numbers in a pair that multiply to give the original number are called factor pairs. For example, the factor pairs of -81 are (1, -81), (3, -27), etc.</li>

114 </ul><ul><li><strong>Factor pairs:</strong>Two numbers in a pair that multiply to give the original number are called factor pairs. For example, the factor pairs of -81 are (1, -81), (3, -27), etc.</li>

116 </ul><ul><li><strong>Prime factorization:</strong>Expressing a number as a product of its prime factors. For example, the prime factorization of -81 is 34.</li>

115 </ul><ul><li><strong>Prime factorization:</strong>Expressing a number as a product of its prime factors. For example, the prime factorization of -81 is 34.</li>

117 </ul><ul><li><strong>Negative factors:</strong>Factors of a number that are negative. For example, the negative factors of -81 are -1, -3, -9, -27, -81.</li>

116 </ul><ul><li><strong>Negative factors:</strong>Factors of a number that are negative. For example, the negative factors of -81 are -1, -3, -9, -27, -81.</li>

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

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

119 <p>▶</p>

118 <p>▶</p>

120 <h2>Hiralee Lalitkumar Makwana</h2>

119 <h2>Hiralee Lalitkumar Makwana</h2>

121 <h3>About the Author</h3>

120 <h3>About the Author</h3>

122 <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>

121 <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>

123 <h3>Fun Fact</h3>

122 <h3>Fun Fact</h3>

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

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