How to do prime factorization?

The process of breaking down a number into its prime factors is called prime factorization.

Let us take an example to understand it better,

Example: Find the prime factorization of 4030.

Using divisibility rules, we know that 

4030 is divisible by 2

• 4030 $\div $ 2 = 2015

2015 is not divisible by 3 because 

• 2 $+$ 0 $+$ 1 $+$ 5 = 8

And, 8 is not divisible by 3. 

However, 2015 is divisible by 5, as it ends with 5. 

• 2015 $\div $ 5 = 403 

Trying out different numbers, it is found that 403 is divisible by 13. 

• 403 $\div $ 13 = 31 

13 and 31 are prime numbers. Factorization ends here.

Hence, we can express 4030 as, 

• 4030 = 2 $\times$ 5 $\times$ 13 $\times$ 31

2, 5, 13, and 31 are the prime factors of 4030.

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Updated on: 10-Oct-2022

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