What are the factors of 108 in pairs?

Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. So, 108 can be derived from smaller number in 6 possible ways using multiplication.

Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. So, 108 can be derived from smaller number in 6 possible ways using multiplication.

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We have all the information you will ever need about the Factors of 108. We will provide you with the definition of Factors of 108, show you how to find the Factors of 108, give you all the Factors of 108, tell you how many Factors 108 has, and supply you with all the Factor Pairs of 108 to prove that our answer is solved correctly.

Factors of 108 definition

The Factors of 108 are all the integers (positive and negative whole numbers) that you can evenly divide into 108. 108 divided by a Factor of 108 will equal another Factor of 108.
How to find the Factors of 108 Since the Factors of 108 are all the numbers that you can evenly divide into 108, we simply need to divide 108 by all numbers up to 108 to see which ones result in an even quotient. When we did that, we found that these calculations resulted in an even quotient: 108 ÷ 1 = 108108 ÷ 2 = 54108 ÷ 3 = 36108 ÷ 4 = 27108 ÷ 6 = 18108 ÷ 9 = 12108 ÷ 12 = 9108 ÷ 18 = 6108 ÷ 27 = 4108 ÷ 36 = 3108 ÷ 54 = 2108 ÷ 108 = 1 The Postive Factors of 108 are therefore all the numbers we used to divide (divisors) above to get an even number. Here is the list of all Postive Factors of 108 in numerical order: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108. Factors of 108 include negative numbers. Therefore, all the Positive Factors of 108 can be converted to negative numbers. The list of Negative Factors of 108 are: -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, and -108.

How many Factors of 108?

When we counted the Factors of 108 that we listed above, we found that 108 has 12 Positive Factors and 12 Negative Factors. Thus, the total number of Factors of 108 is 24.

Factor Pairs of 108

Factor Pairs of 108 are combinations of two factors that when multiplied together equal 108. Here are all the Positive Factor Pairs of 108 1 × 108 = 1082 × 54 = 1083 × 36 = 1084 × 27 = 1086 × 18 = 1089 × 12 = 10812 × 9 = 10818 × 6 = 10827 × 4 = 10836 × 3 = 10854 × 2 = 108108 × 1 = 108 Like we said above, Factors of 108 include negative numbers. Minus times minus equals plus, thus you can convert the Positive Factor Pair list above by simply putting a minus in front of every factor to get all the Negative Factor Pairs of 108: -1 × -108 = 108-2 × -54 = 108-3 × -36 = 108-4 × -27 = 108-6 × -18 = 108-9 × -12 = 108-12 × -9 = 108-18 × -6 = 108-27 × -4 = 108-36 × -3 = 108-54 × -2 = 108-108 × -1 = 108

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Factors of 109

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Factors are pairs of numbers which, if multiplied together, give the original number.

The number 108 is a composite number. So, 108 has more than one factor pair.

These are all the factor pairs of 108:

• 1,108
• 2,54
• 3,36
• 4,27
• 6,18
• 9,12

Here is how to find the factor pairs for the number 108:

• 108 divided by 1 is 108. So, (1, 108) is a factor pair of 108
• 108 divided by 2 is 54. So, (2, 54) is a factor pair of 108
• 108 divided by 3 is 36. So, (3, 36) is a factor pair of 108
• 108 divided by 4 is 27. So, (4, 27) is a factor pair of 108
• 108 divided by 6 is 18. So, (6, 18) is a factor pair of 108
• 108 divided by 9 is 12. So, (9, 12) is a factor pair of 108

Factor pairs of 108 that ads up to a number:

• The factors of 108 that adds up to 109 are 1 and 108
• The factors of 108 that adds up to 110 are 2 and 54
• The factors of 108 that adds up to 111 are 3 and 36
• The factors of 108 that adds up to 112 are 4 and 27
• The factors of 108 that adds up to 114 are 6 and 18
• The factors of 108 that adds up to 117 are 9 and 12

Note 1: if we change the order of all pairs above, we can double the number of pairs. We choose not to show them.
Note 2: do not confuse these pairs with prime factors. See below some info:

The factorization or decomposition of 108 is 22•33.

The prime factors of 108 are 2 and 3. It is the list of the integer's prime factors.

Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54. There are 11 integers that are factors of 108. The biggest factor of 108 is 54. Positive integers that divides 108 without a remainder are listed below.

What are the multiples of 108?

What are the factors of 108 in 2 pairs?

• 1 × 108 = 108
• 2 × 54 = 108
• 3 × 36 = 108
• 4 × 27 = 108
• 6 × 18 = 108
• 9 × 12 = 108
• 12 × 9 = 108
• 18 × 6 = 108
• 27 × 4 = 108
• 36 × 3 = 108
• 54 × 2 = 108

FactorFactor Number

1	one
2	two
3	three
4	four
6	six
9	nine
12	twelve
18	eighteen
27	twenty-seven
36	thirty-six
54	fifty-four

Related Factors

Related Greatest Common Factors of 108

Factors of 108 are the list of integers that we can split evenly into 108. There are overall 12 factors of 108 among which 108 is the biggest factor and 2 and 3 are its prime factors. The Prime Factorization of 108 is 22 × 33.

• Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54 and 108
• Negative Factors of 108: -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54 and -108
• Prime Factors of 108: 2, 3
• Prime Factorization of 108: 2 × 2 × 3 × 3 × 3 = 22 × 33
• Sum of Factors of 108: 280

• The factors of 108 are the numbers which, on dividing 108, leave no remainder.
• 108 is a composite number. It has a total of 12 factors.
• Factors of 108: 1, 2, 3 , 4, 6, 9, 12, 18, 27, 36, 54, and 108.

Explore factors using illustrations and interactive examples.

• Factors of 72: The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
• Factors of 180: The factors of 180 are 1 , 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
• Factors of 19:  The factors of 19 are 1 and 19.
• Factors of 110: The factors of 110 are 1, 2, 5, 10, 11, and 110.
• Factors of 196: The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, and 196.

Let us calculate the factors of 108 using the division method.
When considering numbers that can divide 108 without remainders, we start with 1, then check 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, etc. up to 54 (which is exactly half of 108).

Dividing Remainder

108 ÷ 1	Gives remainder 0. So, 1 is a factor.
108 ÷ 2	Gives remainder 0. So, 2 is a factor.
108 ÷ 3	Gives remainder 0. So, 3 is a factor.
108 ÷ 4	Gives remainder 0.  So, 4 is a factor.
108 ÷ 6	Gives remainder 0. So, 6 is a factor.
108 ÷ 9	Gives remainder 0. So, 9 is a factor.
108 ÷ 12	Gives remainder 0. So, 12 is a factor.
108 ÷ 18	Gives remainder 0.  So, 18 is a factor.
108 ÷ 27	Gives remainder 0. So,  27 is a factor.
108 ÷ 36	Gives remainder 0. So, 36  is a factor.
108 ÷ 54	Gives remainder 0.  So, 54 is a factor.
108 ÷ 108	Gives remainder 0.  So, 108 is a factor.

Prime factorization is finding which prime numbers multiply together to make the original number. 

• The first step is to divide the number 108 with the smallest prime factor, say 2. 108 ÷ 2 = 54 
• Divide 54 again by 2.  54 ÷ 2 = 27 
• Now if we will divide by 2, we will get a fractional number, and a factor cannot be a fraction or a decimal number. So, proceed with the next prime factor, i.e., 3.  27 ÷ 3 = 9 
• Divide again by 3.  9 ÷ 3 = 3 
• And again 3 ÷ 3 = 1 
• Finally, we receive the number 1 at the end of the division process. We cannot proceed further.
• So, the prime factors of 108 are written as  2 × 2 × 3 × 3 × 3, where 2 and 3 are prime numbers.

Finding prime factors by factor tree

The same division process is best represented in the form of a factor tree as given below. A factor tree is a special branching diagram where we find the factors of a number, then the factors of those numbers, etc. until we cannot factorize them anymore. The ends of a factor tree are all the prime factors of the original number.

Pair factors of the number 108 are the two whole numbers that multiply to get 108. Pair factors could be either positive or negative but not a fraction or a decimal number.

• Positive factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108
• Negative factors of 108  -1, -2, -3 , -4, -6, -9, -12, -18, -27, -36, -54, and -108

• Only whole numbers and integers can be factors.
• Only composite numbers can have more than two factors.
• Every factor of a given number is either less than or equal to the given number.
• The number of factors of a given number is finite.

1. Example 1: What is the sum of all the factors of the number 108, including 108?

   Solution:

   Factors of 108: 1, 2, 3 ,4, 6, 9, 12, 18, 27, 36, 54, and 108

   Sum of all the given factors: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 108 = 280

2. Example 2: Find the mean of all the factors of 108. Round it off to two decimal numbers.

   Solution: 

   Factors of 108: 1, 2, 3 ,4, 6, 9, 12, 18, 27, 36, 54, and 108

   Sum of all the given factors : 1+ 2 + 3 + 4 + 6 + 9 + 12+ 18+ 27 + 36 + 54 + 108 = 280

   To calculate the mean we will divide the sum of the  factors with total numbers of factors.

   280 ÷ 12 = 23.33

   Therefore, mean of all the factors of 108 is 23.3

   • Example 3: Find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of 108 and 124.

     Solution:

     The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 and factors of 124 are 1, 2, 4, 31, 62, 124.

     Therefore, the Least Common Multiple (LCM) of 108 and 124 is 3348 and the Greatest Common Factor (GCF) of 108 and 124 is 4.

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The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 and its negative factors are -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, -108.

How Many Factors of 108 are also common to the Factors of 25?

Since, the factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 and factors of 25 are 1, 5, 25. Hence, 108 and 25 have only one common factor which is 1. Therefore, 108 and 25 are co-prime.

What is the Sum of the Factors of 108?

Sum of all factors of 108 = (22 + 1 - 1)/(2 - 1) × (33 + 1 - 1)/(3 - 1) = 280

What is the Greatest Common Factor of 108 and 50?

The factors of 108 and 50 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 and 1, 2, 5, 10, 25, 50 respectively. Common factors of 108 and 50 are [1, 2].

Hence, the GCF of 108 and 50 is 2.

What are the Prime Factors of 108?

The prime factors of 108 are 2, 3.