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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

1.	What Are the Factors of 108?
2.	How to Calculate the Factors of 108?
3.	Factors of 108 by Prime Factorization
4.	Factors of 108 in Pairs

What Are the Factors of 108?

How

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.

How to Calculate the Factors of 108?

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.

Factors of 108 by Prime Factorization

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.

Factor trees of 108

Factors of 108 in Pairs

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

Factors of 108 in pairs

Important Notes:

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.

Factors of 108 Solved Examples

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
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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FAQs on Factors of 108

What are the Factors of 108?

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 = (2^{2 + 1} - 1)/(2 - 1) × (3^{3 + 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.

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