# Prime Factorization Examples

+1 vote
Question: Find the prime factorization of 306.
asked Jun 26, 2013 in Algebra

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Solution:

We need to find the prime factorization of 306.
Step 1:-

Divide the number 306 by first prime number 2.

[306/ 2 ]

By solving above fraction we get the answer as 153. remainder (0).

2 is one of the prime factor of 306
Step 2:-

The answer in the last step is 153. it is not a prime number so divide the number 153 by first prime number 2.

[153/ 2]

By solving the above fraction we get the 76. remainder (1).

Now divide 153 by next prime number 3.

[153/ 3 ]

By solving the above fraction we get the 51. remainder (0).

3 is also one of the prime factor of 306
Step 3 :-

The answer in the last step is 51. it is not a prime number so divide the number 51 by first prime number 2.

[51/ 2]

By solving the above fraction we get the 25. remainder (1).

Now divide 51 by next prime number 3.

[51/ 3 ]

In number system, the prime factors of a positive integer are the prime numbers that divide that integer exactly, without leaving a remainder.
The process of finding these numbers is called integer factorization, or prime factorization.

answered Jun 26, 2013 by ~Rookie~ (159 points)
edited Jul 19, 2013 by smith

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