Question

Prime factorization of 3600 using exponents?

Answer 1

`2^4xx3^2xx5^2`

Explanation:

When doing prime factorization, I like to start with a math fact that I know. For this one, since I can see 36 followed by 2 0s (meaning it's multiplied by 100), I'll start there:

`3600=36xx100`

Neither 36 nor 100 are prime, so let's break those down:

`3600=6xx6xx10xx10`

Still haven't gotten to primes yet:

`3600=2xx3xx2xx3xx2xx5xx2xx5`

This is a long chain of numbers. The exponents will help clean this up:

`3600=2xx3xx2xx3xx2xx5xx2xx5=2^4xx3^2xx5^2`

Answer 2

`2^4xx3^2xx5^2`

Explanation:

`3600 = 36 xx 10^2`

Now, `36 = 2^2xx3^2`

And, `10^2 = 2^2 xx 5^2`

Thus, `3600 = 2^2xx3^2 xx 2^2 xx 5^2`

`= 2^4xx3^2xx5^2`