Prime Factorization

A prime factorization of a natural number is a way of finding factors using only prime numbers as factors. It is also termed complete factorization.

Example 1: Let us find the prime factorization of 140.

By looking at the number, it is divisible by 2, hence we continuously divide 140 by 2 until the quotient is 1.

140 = 2 x 2 x 5 x 7 = 2² x 5 x 7
The prime factors 140 are two 2's, one 5 and one 7.

Another way to find the primes is by using a factor tree.

No matter which factors for 140 you use, the final result is the same.


Example 2: Find the prime factorization of 221.
The number cannot be divided by other numbers except 221 only. That is 221 = 221 x 1.
So the prime factor of 221 is one 221 only since 1 is neither prime nor composite.