In this article, you will learn about the factors of 72, including its common factors as well as positive and negative factors. Here, in this article, we will discuss different methods to determine the factors of 72 step by step.

## What Are The Factors Of 72?

A factor is any number or expression in mathematics that divides on any other number without giving a remainder. Here in terms of 72, its factors are those numbers divisible with it completely without leaving a remainder. In another way, its factors are those numbers that give you the original number 72 when multiplied in pairs.

All factors of 72 are as follows,

Positive Factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Negative Factors: -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -36, -72

Prime Factors of 72: 2 and 3

Sum of factors: 195

## Factors Of 72 In Pairs

Different factors of a number are paired with each other, which will give the original number when the numbers of these pairs are multiplied by each other.

### Positive Pair Factors Of 72

Pair factors of positive 72 are as follows

1 × 72 = 72 (1, 72)

2 × 36 = 72 (2, 36)

3 × 24 = 72 (3, 24)

4 × 18 = 72 (4, 18)

6 × 12 = 72 (6, 12)

8 × 9 = 72 (8, 9)

### Negative Pair Factors Of 72

Pair factors of negative 72 are as follows;

-1 × -72 = 72 (-1, -72)

-2 × -36 = 72 (-2, -36)

-3 × -24 = 72 (-3, -24)

-4 × -18 = 72 (-4, -18)

-6 × -12 = 72 (-6, -12)

-8 × -9 = 72 (-8, -9)

## Factor Tree Of 72

Pic Credit: Study.com

Here we have this factor tree of 72 in which circled numbers are Prime factors of this number. 2 and 3 are the prime number that we obtained through this tree.

## How To Find The Factors Of 72?

There are three different methods of finding factors. Different ways to calculate the factors of 72 are as follows;

Division Method

Multiplication Method

Prime Factorization Method

You can use these methods to find the correct factors of 72. Let’s find out the factors of 72 by using these methods.

### Division Method

In this method, you’ll have to find the divisors that divide with the original number without giving a remainder, so we have to start dividing the original number from 1 and so on to find the exact numbers or factors.

72 ÷ 1 = 72

72 ÷ 2 = 36

72 ÷ 3 = 24

72 ÷ 4 = 18

72 ÷ 6 = 12

72 ÷ 8 = 9

72 ÷ 9 = 8

72 ÷ 12 = 6

72 ÷ 18 = 4

72 ÷ 24 = 3

72 ÷ 36 = 2

72 ÷ 72 = 1

Here, 1,2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72 are the factors of number 72. They will never give a remainder when divided by 72.

### Multiplication Method

In this method, you’ll have to write the number first as a result and then multiply different numbers in a possible way.

72 = 1 × 72

72 = 2 × 36

72 = 3 × 24

72 = 4 × 18

72 = 6 × 12

72 = 8 × 9

72 = 9 × 8

72 = 12 × 6

72 = 18 × 4

72 = 24 × 3

72 = 36 × 2

72 = 72 × 1

So, the factors of 72 through the multiplication method are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

### Prime Factorization Method

In the prime factorization method, you’ll have to start dividing the number with the lowest prime number.

Step 1:

First, divide the number by the lowest prime number, which is 2.

72 ÷ 2 = 36

Step 2:

In the next step, divide the result of the last equation by the lowest prime number, which is 2.

36 ÷ 2 = 18

Step 3:

Now divide the result again with the lowest prime number until it’s divisible by 2.

18 ÷ 2 = 9

Step 4:

Now the result of the last equation is not divisible by 2, so we have to divide it with the next least divisible prime number.

9 ÷ 3 = 3

Step 5:

Again repeat the last step.

3 ÷ 3 = 1

Now we have the least quotient, which is 1, and we can’t further divide it with any other number.

So the prime factors we obtain through the prime factorization method are 2 × 2 × 2 × 3 × 3 = 23 × 32.