Prime Factorization

A number is said to be factorized when a number is expressed as a product of its factors. (Factors are the numbers that we multiply together to get another number.)

Example: 36 = 2 x 18

Here, the given number 36 is factorized and expressed as a product of its factors (i.e. 2 and 18). This is one of the factorizations of 36.

The others are:

In all the above factorizations of 36, we finally arrive at only one factorization 2x2x3x3. In this factorization the only factors 2 and 3 are prime numbers. Such a factorization of a number is called a prime factorization.

In prime factorization, we attempt to find prime numbers which when multiplied together, results in original number.

Steps to find prime factors of given number

Let’s find out the prime factorization of 16.

Step 1: Divide the given number 16 by smallest prime number i.e.2.

            16 ÷ 2 = 8

Step 2: The resultant number is 8, which is a composite number, so we need to divide the number further. Let’s divide the resultant number by 2 (smallest prime number) again.

            8 ÷ 2 = 4

Step 3: Again the resultant number is a composite number, so we need to divide the number further. Again try division by 2.

           4 ÷ 2 = 2

Step 4: The resultant number is a prime number, so we will stop further division. Thus, prime factorization of 16 = 2x2x2x2

Steps to find prime factorization using factor tree method

A factor tree is a tool that helps us to break down the given number into its prime factors. In this method we factorize the given number and we only stop when we can’t find factors any more.

Example 1: Find Prime Factor of 90.

Explanation

First find out 2 factors of the given number 90. Here two factors are 10 and 9. Now look and determine whether these two factors are prime number or not. If it is not a prime number then factor it again. Repeat this process until we get all our factors prime.

The ends are all the prime factors of the original number. Here we see the factor tree of 90 which reveals that 90 = 2 × 5 × 3 × 3.

Question: Find the prime factorization of 300.

Solutions: We divide the number 300 by 2,3,5,7 etc. in this order repeatedly so long as the quotient is divisible by that number.

Thus, the prime factorization of 300 is 2 x 2 x 3 x 5 x 5.