How do you find the prime factorization of 200?

Answer 1

By factoring 200, then factoring each of its factors, until all the factors are primes.

200 = 100 * 2 = (50 * 2) * 2 = (25 * 2) * 2 * 2 = (5 * 5) * 2 * 2 * 2.

As 5 and 2 are both prime, we're done.

Some teachers prefer expressing 5 * 5 * 2 * 2 * 2 in exponential notation so that they don't have to count the digits (they make you do it for them). So write for them this:

5^2 * 2 ^3

Answer 2

To find the prime factorization of 200, start with any two factor pairs of 200 and factor the composite numbers until all factors are prime numbers. For example:

2 x 100

2 x 2 x 50

2 x 2 x 2 x 25

2 x 2 x 2 x 5 x 5