Factors

# Factors of 108 | Prime Factorization of 108 | Factor Tree of 108

Written by Prerit Jain

Updated on: 12 Aug 2023

### Factors of 108 | Prime Factorization of 108 | Factor Tree of 108

Factors of a number are the numbers that divide the original number (in this case 108) evenly, i.e they leave no remainder

These factors can either be negative or positive. However, these factors can’t be decimals or fraction numbers.

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

## What Are the Factors of 108?

The factors of 108 are the numbers that divide 108 exactly without leaving a remainder. Since 108 is a composite number, it means 108 has more than 2 factors, including 1 and the number itself. Moreover, it also means its factors are positive and negative as well. Here the number 108 has both positive and negative factors.

## What Are the Factors of 108 in Pairs?

A pair of numbers when multiplied together will give us 108, as a result, is called pair factor of 108. These pairs are negative and positive. There are 6 pair factors of 108. Let’s see the positive and negative pair factors of 108.

### Positive Pair Factors of 108

The positive pair factors of 108 are (1, 108), (2, 54), (3, 36), (4, 27), (6, 18), and (9, 12).

### Negative Pair Factors of 108

The positive pair factors of 108 are (-1, -108), (-2, -54), (-3, -36), (-4, -27), (-6, -18), and (-9, -12).

You can find the factors of 108 by a division method. In this method, you will find factors of 108 by dividing 108 by all the different consecutive integers. If there is no remainder after being divided by 108, then it will be called a factor of 108. Let’s see this process in detail with the following steps given below.

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

### What Is the Prime Factorization of 108?

By using the prime factorization method, you can find prime factors of 108. In this method, we will divide the number until the quotient is 1. The steps to find prime factors of 150 using the prime factorization method are given below:

Step 1: Firstly, we will divide 108 by 2, as it’s the smallest prime number 108 is divisible by.

108 ÷ 2 = 54

Step 2: Now, we will divide 54 again with 2 as it is also divisible by 2.

54 ÷ 2 = 27

Step 3: As 27 is not divisible by 2, we will move on to the next prime number we can use. We can use 3 this time.

27 ÷ 3 = 9

Step 4: Now, we will divide 9 again with 3 as it can be divided by 3.

9 ÷ 3 = 3

Step 5: Since 3 can only be divided by itself as it’s a prime number, we will use 3 again.

3 ÷ 3 = 1

At last, we have reached 1, so we cannot divide it anymore. Hence, we can see that the prime factors of 108 are 2 X 2 X 3 X 3 X 3 or 22 X 33.

### What Is the Factor Tree of 108?

Students can also use the factor tree method to find the prime factors of 108. In this method, we will place the number 108 at the top of the factor tree. Now, as part of the branches, we will write down set of pair factors of the given number (108). Now, again, we will split the pair of factors into factors. This process will be continued until the branches become prime numbers. Now, circling all the prime numbers will give us the prime factors of 108.

Step 1: Let’s place the number 108 at the top of the factor tree and write down 108 in pairs, that is, 10 and 15.

Step 2: Since 10 is not a prime number, we will now divide 10 into 2 and 5.

Step 3: Since 2 and 5 are prime numbers, we can no longer separate them.

Step 4: As we can see, 15 is not a prime number, so we will split 15 into 3 and 5.

Step 5: We can see that 3 and 5 are both prime numbers. The branches in the factor tree will now be all the prime numbers.

Hence, circling all the branches, 22 X 33 or 2 X 2 X 3 X 3 X 3 = 108, which are 108 prime factors.

There are many ways in which we can write the factor tree of 108. Below is an image representation of the factor tree of 108

## Solved Examples on Factors of 108

What is the sum of all the factors of 108?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108 are the factors of 108.
1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 108 = 280
Hence, 280 is the sum of all factors of 108.

What’s the highest common factor between 108 and 120?
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
Hence, from the above, the common factors of 108 and 120 are 1, 2, 3, 4, 6, and 12.
The highest common factor between 108 and 120 is 12.

What’s the highest common factor between 108 and 54?
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
Factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
Hence, from the above, the common factors of 108 and 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
The highest common factor between 108 and 54 is 25.

Is 75 a factor of 108?
Yes, 36 is a factor of 108.
As 108 ÷ 36 = 3.

What is the largest factor of 108?
The largest factor of 108 is 108.
The second largest factor of 108 is 54.

What are the first 5 factors of 108?
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
The first 5 factors of 108 are 1, 2, 3, 4, and 6.

## FAQs on Factors of 108

What are the factors and prime factors of 108?
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
The prime factors of 108 are 22 X 33 or 2 X 2 X 3 X 3 X 3.

How many 108 factors are odd?
A total of 5 odd numbers are there in factors of 108 and they are 1, 3, 9, 15, and 27.

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

How many pair factors are there in 108?
A total of 6 pairs are there in factors of 108.

What are the composite factors of 108?
4, 6, 9, 12, 18, 27, 36, 54, and 108 are the composite factors of 108.
Composite factors are those that have more than 2 factors other than 1 and itself.

What are the positive factors of 108?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108 are the positive factors of 108.

Now that you have all the necessary information regarding the factors of 108, We hope this blog has been useful for you and easy to understand as well.

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Prerit Jain

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