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

3 <p>Factors of any number are the whole numbers that can divide the number completely. Why are factors important to learn? For mathematical approaches, factors are used in organizing and bringing more efficiency to any task. In this article, let's learn how to solve factors of 78 easily.</p>

4 <h2>What are the Factors of 78?</h2>

5 <p>Factors<a>of</a>78 are those<a>numbers</a>that can divide 78 perfectly. The<a>factors</a>of 78 are:</p>

6 <p>1,2,3,6,13,26,39, and 78.</p>

7 <ul><li><strong>Negative factors of 78:</strong>-1, -2, -3 -6, -13, -26, -39, -78</li>

8 </ul><ul><li><strong>Prime factors of 78:</strong>2,3</li>

9 </ul><ul><li><strong>Prime factorization of 78:</strong>3×2×13</li>

10 </ul><ul><li><strong>The<a>sum</a>of factors of 78:</strong>1+2+3+6+13+26+39+78= 168</li>

11 </ul><h2>How to Find the Factors of 78</h2>

12 <p>For finding factors of 78, 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><h3>Finding Factors using Multiplication Methods</h3>

18 <p>This particular method often finds the pair of factors which, on<a>multiplication</a>together, produces 78. Let us find the pairs which, on multiplication, yields 78.</p>

19 <p>1×78=78</p>

20 <p>2×39=78</p>

21 <p>3×26=78</p>

22 <p>6×13=78</p>

23 <p>From this, we conclude that, factors of 78 are:1,2,3,6,13,26,39, and 78. </p>

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26 <h3>Finding Factors using Division Method</h3>

25 <h3>Finding Factors using Division Method</h3>

27 <p>The<a>division</a>method finds the numbers that evenly divides the given number 78. To find the factors of 78, we have to divide 78 by all possible<a>natural numbers</a><a>less than</a>78 and check.</p>

26 <p>The<a>division</a>method finds the numbers that evenly divides the given number 78. To find the factors of 78, we have to divide 78 by all possible<a>natural numbers</a><a>less than</a>78 and check.</p>

28 <p>1,2,3,6,13,26,39,78 are the only factors that the number 78 has. So to verify the factors of 78 using the division method, we just need to divide 78 by each factor.</p>

27 <p>1,2,3,6,13,26,39,78 are the only factors that the number 78 has. So to verify the factors of 78 using the division method, we just need to divide 78 by each factor.</p>

29 <p>78/1 =78</p>

28 <p>78/1 =78</p>

30 <p>78/2 =39</p>

29 <p>78/2 =39</p>

31 <p>78/3=26</p>

30 <p>78/3=26</p>

32 <p>78/6=13</p>

31 <p>78/6=13</p>

33 <p>78/13=6</p>

32 <p>78/13=6</p>

34 <p>78/26=3</p>

33 <p>78/26=3</p>

35 <p>78/39=2</p>

34 <p>78/39=2</p>

36 <p>78/78=1</p>

35 <p>78/78=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 78 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 78 into a<a>product</a>of its prime<a>integers</a>.</p>

39 <p>Prime Factors of 78: 2,3.</p>

38 <p>Prime Factors of 78: 2,3.</p>

40 <p>Prime Factorization of 78: 3×2×13 </p>

39 <p>Prime Factorization of 78: 3×2×13 </p>

41 <h3>Factor tree</h3>

40 <h3>Factor tree</h3>

42 <p>The number 78 is written on top and two branches are extended.</p>

41 <p>The number 78 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., 78.</p>

42 <p>Fill in those branches with a factor pair of the number above,<a>i</a>.e., 78.</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 78 are 2 and 39, then proceeding to 39, we get 3 and 13. </p>

44 <p>The first two branches of the<a>factor tree</a>of 78 are 2 and 39, then proceeding to 39, we get 3 and 13. </p>

46 <p><strong>Factor Pairs</strong></p>

45 <p><strong>Factor Pairs</strong></p>

47 <p>Positive pair factors: (1,78), (2,39), (3,26), (6,13)</p>

46 <p>Positive pair factors: (1,78), (2,39), (3,26), (6,13)</p>

48 <p>Negative pair factors: (-1,-78), (-2,-39), (-3,-26), (-6,-13). </p>

47 <p>Negative pair factors: (-1,-78), (-2,-39), (-3,-26), (-6,-13). </p>

49 <h2>Common Mistakes and How to Avoid Them in Factors of 78</h2>

48 <h2>Common Mistakes and How to Avoid Them in Factors of 78</h2>

50 <p>Children quite often make silly mistakes while solving factors. Let us see what are the common errors to occur and how to avoid them</p>

49 <p>Children quite often make silly mistakes while solving factors. Let us see what are the common errors to occur and how to avoid them</p>

50 + <h2>Download Worksheets</h2>

51 <h3>Problem 1</h3>

52 <p>Find the GCF of 78 and 75</p>

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

54 <p> Factors of 78: 1,2,3,6,13,26,39,78</p>

55 <p>Factors of 75: 1,3,5,15,25,75</p>

56 <p>Common factors of 78 and 75: 1,3</p>

57 <p>So, the Greatest Common Factor of 78 and 75 is 3.</p>

58 <p>Answer: 3 </p>

59 <h3>Explanation</h3>

60 <p> We first listed out the factors of 75 and 78 and then found the common factors and then identified the greatest common factor from the common list. </p>

61 <p>Well explained 👍</p>

62 <h3>Problem 2</h3>

63 <p>Find the smallest number which, when divided by 26,39 and 78, leaves a remainder 3 in each case.</p>

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

65 <p>First finding the LCM of 26,39,78</p>

66 <p>Prime factorization of 26 =13×2</p>

67 <p>Prime factorization of 39 = 13×3</p>

68 <p>Prime factorization of 78 = 3×2×13</p>

69 <p>LCM of 26,39,78 = 13×2×3=78</p>

70 <p>The smallest number which, when divided by 26,39 and 78, leaves a remainder 3 in each case is = LCM + 3 = 78+3 =81</p>

71 <p>Answer: 81 </p>

72 <h3>Explanation</h3>

73 <p>First find the LCM and just add the remainder with that to get the smallest number. </p>

74 <p>Well explained 👍</p>

75 <h3>Problem 3</h3>

76 <p>The area of a rectangle is 78 square units. If the length is 13 units, then what is the measure of its width?</p>

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

78 <p>Area of rectangle: 78 sq units</p>

79 <p>Factors of 78: 1,2,3,6,13,26,39,78</p>

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

81 <p>Given, length= 13 units</p>

82 <p>There exists a factor pair of 78, which is (6,13). Hence, width is 6 units. Let’s check it through the formula for area.</p>

83 <p>So, length×width = area</p>

84 <p>⇒ 13 × width = 78</p>

85 <p>⇒ width = 78/13 = 6</p>

86 <p>Answer: 6 units </p>

87 <h3>Explanation</h3>

88 <p>Used the concept of factor pairs for 78 and rechecked using the formula for finding area of a rectangle. </p>

89 <p>Well explained 👍</p>

90 <h3>Problem 4</h3>

91 <p>Find the smallest number that is divisible by 2,6,26.</p>

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

93 <p>Prime factorization of 2: 2×1.</p>

94 <p>Prime factorization of 6: 3×2</p>

95 <p>Prime factorization of 26: 13×2</p>

96 <p>LCM of 2,6,26: 2×3×13 = 78</p>

97 <p>Answer: 78 is the smallest number which is divisible by 2,6, and 26. </p>

98 <h3>Explanation</h3>

99 <p>To find the smallest number which is divisible by 2,6,26, we need to find the LCM of these numbers. </p>

100 <p>Well explained 👍</p>

101 <h3>Problem 5</h3>

102 <p>What is the sum of the factors of 78 and 79?</p>

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

104 <p>Factors of 78: 1,2,3,6,13,26,39,78</p>

105 <p>Sum of the factors: 1+2+3+6+13+26+39+78= 168</p>

106 <p>Factors of 79: 1,79</p>

107 <p>Sum of the factors: 1+79 =80 </p>

108 <h3>Explanation</h3>

109 <p>Added all the factors togather to get the sum.</p>

110 <p>Well explained 👍</p>

111 <h2>FAQs on Factors of 78</h2>

112 <h3>1.What are the multiples of 78?</h3>

113 <p>The multiples of 78 are: 78,156,234,312,390,468,.... </p>

114 <h3>2.What times table equals 78?</h3>

115 <p>78 comes in 2 times and 39<a>tables</a>: 2×39 =78.</p>

116 <p>78 comes in 3 times and 26 times table: 3×26 =78.</p>

117 <p>78 comes in 6 times and 13 times table: 6×13 =78. </p>

118 <h3>3.Is 78 divisible by 7?</h3>

119 <p>78 is not divisible by 7. It leaves a remainder of 1. </p>

120 <h3>4.What are all 79 factors?</h3>

121 <p> Factors of 79 are: 1 and 79. </p>

122 <h3>5.What is the LCM of 78 and 104?</h3>

123 <p>Prime factorization of 78 = 3×2×13</p>

124 <p>Prime factorization of 104 =23×13</p>

125 <p>LCM of 78 and 104= 13×23×3=312 </p>

126 <h2>Important Glossaries for Factors of 78</h2>

127 <ul><li><strong>Ratio -</strong>Ratio of two numbers compares between them, how many times one number contains the other number. It is expressed as m:n, where m and n are two positive numbers whose ratio is to be shown.</li>

128 </ul><ul><li><strong>Factors -</strong>These are numbers that divide the given number without leaving any remainder or the remainder as 0.</li>

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

130 </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>

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

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

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

134 <p>▶</p>

135 <h2>Hiralee Lalitkumar Makwana</h2>

136 <h3>About the Author</h3>

137 <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>

138 <h3>Fun Fact</h3>

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