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2 <p>Last updated on<strong>December 11, 2025</strong></p>

3 <p>Factors of any number are the dividers or multipliers that can divide the number fully and can be multiplied together to produce the given product, 165. Do you know, factors form the basic approach to solve some general mathematical procedures? This article will give you the insights of factors of 165.</p>

4 <h2>What are the Factors of 165?</h2>

5 <p>The<a>factors</a><a>of</a>165 or the<a>numbers</a>which divide 165 exactly are:</p>

6 <p>1,3,5,11,15,33,55, and 165.</p>

7 <p><strong>Negative factors of 165:</strong>-1,-3,-5,-11,-15,-33,-55,-165.</p>

8 <p><strong>Prime factors of 165:</strong>3,5,11</p>

9 <p><strong>Prime factorization of 165:</strong>3×5×11</p>

10 <p><strong>The<a>sum</a>of factors of 165:</strong>1+3+5+11+15+33+55+165= 288 </p>

11 <h2>How to Find the Factors of 165</h2>

12 <p>For finding factors of 165, we will be learning these below-mentioned methods:</p>

13 <ul><li>Multiplication Method</li>

14 </ul><ul><li>Division Method</li>

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

16 </ul><ul><li>Factor Tree </li>

17 </ul><h2>Finding Factors using Multiplication Methods</h2>

18 <p>This particular method often finds the pair of factors which, on<a>multiplication</a>together, produces 165. Let us find the pairs which, on multiplication, yields 165.</p>

19 <p>1×165=165</p>

20 <p>3×55=165</p>

21 <p>5×33=165</p>

22 <p>11×15=165</p>

23 <p>So, factors of 165 are: 1,3,5,11,15,33,55, and 165. </p>

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26 <h2>Finding Factors using Division Method</h2>

25 <h2>Finding Factors using Division Method</h2>

27 <p>The<a>division</a>method finds the factors that evenly divides the given number 165. In this process, we have to divide 165 by all possible<a>natural numbers</a><a>less than</a>165 and check.</p>

26 <p>The<a>division</a>method finds the factors that evenly divides the given number 165. In this process, we have to divide 165 by all possible<a>natural numbers</a><a>less than</a>165 and check.</p>

28 <p>1,3,5,11,15,33,55, and 165 are the only factors that the number 165 has. So to verify the factors of 165 using the division method, we just need to divide 165 by each factor.</p>

27 <p>1,3,5,11,15,33,55, and 165 are the only factors that the number 165 has. So to verify the factors of 165 using the division method, we just need to divide 165 by each factor.</p>

29 <p>165/1 =165</p>

28 <p>165/1 =165</p>

30 <p>165/3=55</p>

29 <p>165/3=55</p>

31 <p>165/5=33</p>

30 <p>165/5=33</p>

32 <p>165/11=15</p>

31 <p>165/11=15</p>

33 <p>165/15=11</p>

32 <p>165/15=11</p>

34 <p>165/33=5</p>

33 <p>165/33=5</p>

35 <p>165/55=3</p>

34 <p>165/55=3</p>

36 <p>165/165=1</p>

35 <p>165/165=1</p>

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

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

38 <p>Prime Factorization is the easiest process to<a>find prime factors</a>. It decomposes 165 into a<a>product</a>of its prime<a>integers</a>.</p>

37 <p>Prime Factorization is the easiest process to<a>find prime factors</a>. It decomposes 165 into a<a>product</a>of its prime<a>integers</a>.</p>

39 <p>Prime Factors of 165: 3,5,11.</p>

38 <p>Prime Factors of 165: 3,5,11.</p>

40 <p>Prime Factorization of 165: 3×5×15 </p>

39 <p>Prime Factorization of 165: 3×5×15 </p>

41 <h2>Factor tree</h2>

40 <h2>Factor tree</h2>

42 <p> The number 165 is written on top and two branches are extended.</p>

41 <p> The number 165 is written on top and two branches are extended.</p>

43 <p>Fill in those branches with a factor pair of the number above,<a>i</a>.e., 165.</p>

42 <p>Fill in those branches with a factor pair of the number above,<a>i</a>.e., 165.</p>

44 <p>Continue this process until each branch ends with a prime factor (number).</p>

43 <p>Continue this process until each branch ends with a prime factor (number).</p>

45 <p>The first two branches of the<a>factor tree</a>of 165 are 3 and 55, then proceeding to 55, we get 5 and 11. So, now the factor tree for 165 is achieved. </p>

44 <p>The first two branches of the<a>factor tree</a>of 165 are 3 and 55, then proceeding to 55, we get 5 and 11. So, now the factor tree for 165 is achieved. </p>

46 <h2>Factor Pairs</h2>

45 <h2>Factor Pairs</h2>

47 <p><strong>Positive pair factors:</strong> (1,165), (3,55), (5,33), (11,15).</p>

46 <p><strong>Positive pair factors:</strong> (1,165), (3,55), (5,33), (11,15).</p>

48 <p><strong>Negative pair factors:</strong> (-1,-154), (-3,-55), (-5,-33), (-11,-15). </p>

47 <p><strong>Negative pair factors:</strong> (-1,-154), (-3,-55), (-5,-33), (-11,-15). </p>

49 <h2>Common Mistakes and How to Avoid Them in Factors of 165</h2>

48 <h2>Common Mistakes and How to Avoid Them in Factors of 165</h2>

50 <p>Solving problems based on factors can, sometimes, lead to misconceptions among children. Let us check what the common errors are and how to avoid them. </p>

49 <p>Solving problems based on factors can, sometimes, lead to misconceptions among children. Let us check what the common errors are and how to avoid them. </p>

50 + <h2>Download Worksheets</h2>

51 <h3>Problem 1</h3>

52 <p>A lady has 165 dahlias and 55 roses. She wants to divide them equally among some vases. What is the maximum number of vases she requires?</p>

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

54 <p> Number of dahlias: 165</p>

55 <p>Number of roses: 55</p>

56 <p>Factors of 165: 1,3,5,11,15,33,55,165</p>

57 <p>Factors of 55: 1,5,11,55</p>

58 <p>Common factors of 165 and 55: 1,5,11,55.</p>

59 <p>Greatest common factor of 165 and 55: 55</p>

60 <p>So, there will be 55 vases she requires.</p>

61 <p>Answer: 55 vases </p>

62 <h3>Explanation</h3>

63 <p> To divide equally, the maximum number of plates can be found through the Greatest Common Factor. Here, we found the GCF, which is the answer. </p>

64 <p>Well explained 👍</p>

65 <h3>Problem 2</h3>

66 <p>Find the simplest form of square root of 165.</p>

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

68 <p>√165 = √(3×5×11) = √165</p>

69 <p>Answer: The simplest form of square root of 165 is √165. </p>

70 <h3>Explanation</h3>

71 <p>Break down 165 into its product of its prime factor and find its square root by grouping a pair of factors at a time, leaving the remaining single factors under radical. </p>

72 <p>Well explained 👍</p>

73 <h3>Problem 3</h3>

74 <p>The area of a rectangle is 165 square units. If the length is 33 units, then what is the measure of its width?</p>

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

76 <p>Area of rectangle: 165 sq units</p>

77 <p>Factors of 165: 1,3,5,11,15,33,55,165</p>

78 <p>We know that the area of a rectangle is the product of its length and breadth.</p>

79 <p>Given, length= 33 units</p>

80 <p>There exists a factor pair of 165, which is (5,33). Hence, width is 5 units. Let’s check it through the formula for area.</p>

81 <p>So, length×width = area</p>

82 <p>⇒ 33 × width = 165</p>

83 <p>⇒ width = 165/33 = 5</p>

84 <p>Answer: 5 units </p>

85 <h3>Explanation</h3>

86 <p>Used the concept of factor pairs for 165 and rechecked using the formula for finding area of a rectangle. </p>

87 <p>Well explained 👍</p>

88 <h3>Problem 4</h3>

89 <p>Find the smallest number that is divisible by 5 and 33.</p>

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

91 <p>Prime factorization of 5: 5×1.</p>

92 <p>Prime factorization of 33: 3×11</p>

93 <p>LCM of 5 and 33: 3×5×11 = 165</p>

94 <p>Answer: 165 is the smallest number which is divisible by 5 and 33</p>

95 <h3>Explanation</h3>

96 <p>To find the smallest number which is divisible by 5 and 33, we need to find the LCM of these numbers. </p>

97 <p>Well explained 👍</p>

98 <h3>Problem 5</h3>

99 <p>If a number is divisible by both 3 and 55, is it divisible by 165?</p>

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

101 <p>Yes, any number which is divisible by 3 and 55 is also divisible by 165, since 165 = 3×55</p>

102 <p>Answer: Yes </p>

103 <h3>Explanation</h3>

104 <p>Any number which is divisible by the factor 3 and factor 55 of 165, then it is also divisible by 165 because 165 is a product of 3 and 55.</p>

105 <p>Well explained 👍</p>

106 <h2>FAQs on Factors of 165</h2>

107 <h3>1.What is 165 divided by prime numbers?</h3>

108 <p>165 has factors 1,3,5,11,15,33,55,165. Out of these factors, three are<a>prime numbers</a>or prime factors and the rest are composite factors. The prime factors are: 3,5,11. </p>

109 <h3>2.Is 11 a factor of 165?</h3>

110 <p>The list of factors of 165 are: 1,3,5,11,15,33,55,165, where we can see that 11 is in the list. Hence, 11 is a factor of 165. Let’s check this: 165/11=15. </p>

111 <h3>3.Can 165 be divided by 3?</h3>

112 <p>The list of factors of 165 are: 1,3,5,11,15,33,55,165, where we can see that 3 is in the list. Hence, 3 is a factor of 165. Let’s check this: 165/3=55. </p>

113 <h3>4.Is 165 divisible by 6?</h3>

114 <p>To check the divisibility test of 6, we have to divide 165 first with 2 and 3 separately. If 165 is divisible by 2 and 3, it is also divisible by 6. 165 is not an<a>even number</a>, so it is not divisible by 2, but 1+6+5=12 is divisible by 3, and hence 165 is divisible by 3. We conclude that 165 is not divisible by 6. </p>

115 <h3>5.Is 165 divisible by 4?</h3>

116 <p>We know that a number is divisible by 4 if its last two digits are compactly divisible by 4 or are zeroes. For 165, the last two digits are 65, which is not divisible by 4. Hence, 165 is not divisible by 4. </p>

117 <h2>Important Glossaries for Factors of 165</h2>

118 <ul><li><strong>Multipliers -</strong>Number which multiplies or a number by which another number is multiplied.</li>

119 </ul><ul><li><strong>Dividers -</strong>A number that divides.</li>

120 </ul><ul><li><strong>Prime Factorization -</strong>It involves factoring the number into its prime factors.</li>

121 </ul><ul><li><strong>Prime factors -</strong>These are the prime numbers which on multiplication together results into the original number whose prime factors are to be obtained.</li>

122 </ul><ul><li><strong>Composite numbers -</strong>These are numbers having more than two factors.</li>

123 </ul><ul><li><strong>Multiple -</strong>It is a product of the given number and any other integer.</li>

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

125 <p>▶</p>

126 <h2>Hiralee Lalitkumar Makwana</h2>

127 <h3>About the Author</h3>

128 <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>

129 <h3>Fun Fact</h3>

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