Question

How do I express 108 as a product of prime factors?

Answer 1

`2^2 xx 3^3= 108`

Explanation:

Search for all the primes it's divisible by.

As it is even, it is divisible by 2.

`108/2=54`

54 is also divisible by 2.

`108/2^2=54/2=27`

You may recognize 27 as being equal to `3^3`. (If you get a less obvious number then you can simply guess primes smaller than this until you find one that divides it or use division algorithms etc).

So, we divided 108 by `2^2` and `3^3` which gives us `1`.

These two numbers are powers of primes that when multiplied give us 108:

`2^2 xx 3^3= 108`

Answer 2

`108=2xx2xx3xx3xx3=2^2xx3^3`

Explanation:

split the number into a product pair with at least one of them being prime. Then split the non-prime number into a product pair again. Continue until all the factors are prime numbers.

`108=color(blue)(2)xx54`

`108=2xxcolor(blue)(2)xx27`

`108=2xx2xxcolor(blue)(3)xx9`

`108=2xx2xx3xx3xx3`

`108=2xx2xx3xx3xx3=2^2xx3^3`

Answer 3

`108 = 2^2 xx 3^3`

Explanation:

You can start with any two factors of `108` and break them into smaller and smaller factors, until they are all prime numbers,

`108 = " "12 " "xx 9`

`108 = 4xx3" "xx3xx3`

`108 = 2xx2xx3xx3xx3`

`108 = 2^2 xx 3^3`