# What are all the factors, the prime factorization, and factor pairs of 252?

To find the factors of 252, divide 252 by each number starting with 1 and working up to 252

## 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 252 ?

To calculate the factors of 252 , you can use the division method.

1. Begin by dividing 252 by the smallest possible number, which is 2.

2. If the division is even, then 2 is a factor of 252.

3. Continue dividing 252 by larger numbers until you find an odd number that does not divide evenly into 252 .

4. The numbers that divide evenly into 252 are the factors of 252 .

Now let us find how to calculate all the factors of Two hundred fifty-two :

252 ÷ 1 = 252
252 ÷ 2 = 126
252 ÷ 3 = 84
252 ÷ 4 = 63
252 ÷ 6 = 42
252 ÷ 7 = 36
252 ÷ 9 = 28
252 ÷ 12 = 21
252 ÷ 14 = 18
252 ÷ 18 = 14
252 ÷ 21 = 12
252 ÷ 28 = 9
252 ÷ 36 = 7
252 ÷ 42 = 6
252 ÷ 63 = 4
252 ÷ 84 = 3
252 ÷ 126 = 2
252 ÷ 252 = 1

As you can see, the factors of 252 are 1 , 2 , 3 , 4 , 6 , 7 , 9 , 12 , 14 , 18 , 21 , 28 , 36 , 42 , 63 , 84 , 126 and 252 .

## How many factors of 252 are there ?

The factors of 252 are the numbers that can evenly divide 252 . These numbers are 1 , 2 , 3 , 4 , 6 , 7 , 9 , 12 , 14 , 18 , 21 , 28 , 36 , 42 , 63 , 84 , 126 and 252.

Thus, there are a total of 18 factors of 252

## What are the factor pairs of 252 ?

Factor Pairs of 252 are combinations of two factors that when multiplied together equal 252. There are many ways to calculate the factor pairs of 252 .

One easy way is to list out the factors of 252 :
1 , 2 , 3 , 4 , 6 , 7 , 9 , 12 , 14 , 18 , 21 , 28 , 36 , 42 , 63 , 84 , 126 , 252

Then, pair up the factors:
(1,252),(2,126),(3,84),(4,63),(6,42),(7,36),(9,28),(12,21) and (14,18) These are the factor pairs of 252 .

## Prime Factorisation of 252

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 252 using a factor tree, we would start by writing 252 on a piece of paper. Then, we would draw a line under it and begin finding factors.

The final prime factorization of 252 would be 2 x 2 x 3 x 3 x 7.

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 252 using this method, we keep dividing until it gives a non-zero remainder.

252 ÷ 2 = 126
126 ÷ 2 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1

So the prime factors of 252 are 2 x 2 x 3 x 3 x 7.

## Frequently Asked Questions on Factors

### What are all the factors of 252 ?

The factors of 252 are 1 , 2 , 3 , 4 , 6 , 7 , 9 , 12 , 14 , 18 , 21 , 28 , 36 , 42 , 63 , 84 , 126 and 252.

### What is the prime factorization of 252 ?

The prime factorization of 252 is 2 x 2 x 3 x 3 x 7 or 22 x 32 x 71, where 2 , 3 , 7 are the prime numbers .

### What are the prime factors of 252 ?

The prime factors of 252 are 2 , 3 , 7 .

### Is 252 a prime number ?

A prime number is a number that has only two factors 1 and itself.
252 it is not a prime number because it has the factors 1 , 2 , 3 , 4 , 6 , 7 , 9 , 12 , 14 , 18 , 21 , 28 , 36 , 42 , 63 , 84 , 126 and 252.