# Prime Factorization

Prime factorization is a method in which we determine the factors of any given number that are all prime numbers only. Before that, you need to know what a prime number is.

A prime number is a number that is divisible only by itself and 1. Take for example the following numbers, 1,3,5,7,11,13,17… These numbers are not divisible by any other numbers except they are divisible only by 1 or the number itself.

Let’s take the example of 15, the factors of 15 can be 15×1, 3×5, but 1 is not a prime number and the prime factors of 15 is 3 and 5.

## How to Determine the Prime Factorization of a Number

When it comes to finding the prime factorization of a number, we can determine using a very simple way. Let’s say we need to determine the prime factorization of 48. Let’s use a factor tree and start dividing the number by 2 until you have only prime numbers left as shown above in the diagram.
48 is an even number and when you divide it by 2, you get 24 and when you further divide you get 12, 6 and finally 3. The prime numbers factors that you get 2 * 2 * 2 * 3

All these number are prime numbers only and the prime factorization is found easily with the factor tree method.

### Example 1: What is the prime factorization of 147?

Dividing 147 by the first prime number,

147/2 = 73.5, but since 73.5 is not a whole number, we can try using the next prime number

147 / 3 = 49

We get 49 and let’s try to divide 49 by prime numbers. 7 is the least prime number that divides 49

49 = 7 x7

7 is a prime number.

Hence the prime factorization for 147 = 3 * 7 * 7

### Example 2: What is the prime factorization of 90?

To find out the prime factorization of 90, we divide it with the first prime number

90 / 2 = 45

Next dividing 45 /2 will not give you a whole number hence, we can divide by 3

45 / 3 = 15

Next divide 15 by 3

15 / 3 = 5

5 is a prime number and hence the prime factorization for 90 is

2 * 3 * 3 * 5