# What are all the factors, the prime factorization, and factor pairs of 72?

To find the factors of 72, divide 72 by each number starting with 1 and working up to 72

## What is a factor in math ?

Factors are the numbers you multiply together to get another number. For example, the factors of 15 are 3 and 5 because 3 × 5 = 15.

The factors of a number can be positive or negative, but they cannot be zero.

The factors of a number can be used to find out if the number is prime or not.

A prime number is a number that has only two factors: itself and 1. For example, the number 7 is prime because its only factors are 7 and 1.

## List all of the factors of 72 ?

To calculate the factors of 72 , you can use the division method.

1. Begin by dividing 72 by the smallest possible number, which is 2.

2. If the division is even, then 2 is a factor of 72.

3. Continue dividing 72 by larger numbers until you find an odd number that does not divide evenly into 72 .

4. The numbers that divide evenly into 72 are the factors of 72 .

Now let us find how to calculate all the factors of Seventy-two :

72 ÷ 1 = 72
72 ÷ 2 = 36
72 ÷ 3 = 24
72 ÷ 4 = 18
72 ÷ 6 = 12
72 ÷ 8 = 9
72 ÷ 8 = 9
72 ÷ 9 = 8
72 ÷ 12 = 6
72 ÷ 18 = 4
72 ÷ 24 = 3
72 ÷ 36 = 2
72 ÷ 72 = 1

As you can see, the factors of 72 are 1 , 2 , 3 , 4 , 6 , 8 , 8 , 9 , 12 , 18 , 24 , 36 and 72 .

## How many factors of 72 are there ?

The factors of 72 are the numbers that can evenly divide 72 . These numbers are 1 , 2 , 3 , 4 , 6 , 8 , 8 , 9 , 12 , 18 , 24 , 36 and 72.

Thus, there are a total of 13 factors of 72

## What are the factor pairs of 72 ?

Factor Pairs of 72 are combinations of two factors that when multiplied together equal 72. There are many ways to calculate the factor pairs of 72 .

One easy way is to list out the factors of 72 :
1 , 2 , 3 , 4 , 6 , 8 , 8 , 9 , 12 , 18 , 24 , 36 , 72

Then, pair up the factors:
(1,72),(2,36),(3,24),(4,18),(6,12) and (8,9) These are the factor pairs of 72 .

## Prime Factorisation of 72

There are a few different methods that can be used to calculate the prime factorization of a number. Two of the most common methods are listed below.

1) Use a factor tree :

1. Take the number you want to find the prime factorization of and write it at the top of the page

2. Find the smallest number that goes into the number you are finding the prime factorization of evenly and write it next to the number you are finding the prime factorization of

3. Draw a line under the number you just wrote and the number you are finding the prime factorization of

4. Repeat step 2 with the number you just wrote until that number can no longer be divided evenly

5. The numbers written on the lines will be the prime factors of the number you started with

For example, to calculate the prime factorization of 72 using a factor tree, we would start by writing 72 on a piece of paper. Then, we would draw a line under it and begin finding factors.

The final prime factorization of 72 would be 2 x 2 x 2 x 3 x 3.

2) Use a factorization method :

There are a few different factorization methods that can be used to calculate the prime factorization of a number.

One common method is to start by dividing the number by the smallest prime number that will divide evenly into it.

Then, continue dividing the number by successively larger prime numbers until the number has been fully factorised.

For example, to calculate the prime factorization of 72 using this method, we keep dividing until it gives a non-zero remainder.

72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So the prime factors of 72 are 2 x 2 x 2 x 3 x 3.

## Frequently Asked Questions on Factors

### What are all the factors of 72 ?

The factors of 72 are 1 , 2 , 3 , 4 , 6 , 8 , 8 , 9 , 12 , 18 , 24 , 36 and 72.

### What is the prime factorization of 72 ?

The prime factorization of 72 is 2 x 2 x 2 x 3 x 3 or 23 x 32, where 2 , 3 are the prime numbers .

### What are the prime factors of 72 ?

The prime factors of 72 are 2 , 3 .

### Is 72 a prime number ?

A prime number is a number that has only two factors 1 and itself.
72 it is not a prime number because it has the factors 1 , 2 , 3 , 4 , 6 , 8 , 8 , 9 , 12 , 18 , 24 , 36 and 72.