Factors of 108

In mathematical terms, 108 is said to be a composite number. In this chapter, you will be made familiar with all the factors and factor pairs of 108, so it proves that your answer is solved correctly. That said, let’s get to know the factors for 108 that are as shown in the table given below:

Following are the factors of 108:

All Factors of 108

How Many Factors of 108 are There?

You should get the count for factors from above, you will find that 108 has 12 positive factors and 12 negative factors. Hence, the total number of factors of 108 is 24.

What is the Definition of Factors of 108?

The factors of 108 consist of all the integers (positive as well as negative whole numbers) that we are able to divide into 108. That being said, 108 divided by a factor of 108 will be equivalent to another factor of 108.

Prime Factorization of 108

A prime factorization is an outcome of factoring a number into a set of constituents in which every member is a prime number. This is usually written by displaying 108 as a product of its prime factors. 

This is also called the prime factorization; the smallest prime number in this series is defined as the smallest prime factor. 

Prime factorization: 108 = 2 x 2 x 3 x 3 x 3, 

This can also be mathematically written as 108 = 2² x 3³.

Because the factors of 108 are all the numbers (positive and negative numbers) that are evenly divided into 108, we simply require to divide 108 by all numbers up to 108 to find out which ones lead up to an even quotient. Let’s perform the operation of division to find out which calculations outcomes in even quotient:

How to Find the Factors of 108

Positive Factors of 108

The positive factors of 108 are thus all the mathematical numbers we used to divide to obtain an even number. Below are all the positive factors of 108 arranged in numerically ascending order:

1

2

3

4

6

9

12

18

27

36

54

108

Negative Factors of 108

There are also negative numbers for factors of 108. Hence, all the positive factors of 108 can be transformed into negative numbers. Below are all the negative factors of 108 arranged in numerically ascending order:

−1

−2

  3

−4

−6

−9

−12

−18

−27

−36

−54

−108

Solved Examples

Example1: Determine the sum of all the factors of 108, including 108?

Solution: Factors of 108 are given below:

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

Now, sum up all the factors

1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 108 = 280

Hence, the total of all factors of the number 108 = 280

Example 2:

Evaluate the mean of all the factors of the number 108. Take the answer in the round off to two decimal places.

Solution:

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

Sum = 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 108 = 280

In order to find out the mean, we will divide the sum of factors by the total number of factors, with which we get,

\[\frac {280} {12}\] = 23.33.