What are the factors of 90?

First, because 90 is an even number we can factor out a 2:

`90 = 2 xx 45`

Because 45 ends in a 5 it is divisible by 5 so we can factor out a 5:

`90 = 2 xx 5 xx 9`

We know 9 is divisible by 3 so we can factor our a 3:

`90 = 2 xx 5 xx 3 xx 3`

or

`90 = 2 xx 3 xx 3 xx 5`

When dealing with factors, you can list all the factors, or write a number as the product of the prime factors.

If you know the product of the prime factors you can use those to determine all the other factors.

`90 = 10 xx9`

`:. 90 = 2xx5xx3xx3 " "= 2xx3xx3xx5`

Listing the factors using these prime factors can be done as follows:

`1` at a time: `1, 2,3,5`
Product of `2` prime factors at a time: `6,10,9,15`
Product of `3` prime factors at a time: `18,30, 45`
Product of `4` prime factors at a time: `90`

The factors work in pairs, a big one with a small one.

Half of the factors are smaller than `sqrt90` and half are bigger.
`sqrt90 = 9. ....`

In order they are:

`1," "2," "3," "5," "6," "9," "10," "15," "18," "30," "45," "90`
`color(white)(xxxxxxxxccccxxxx.xxxxx)uarr`
`color(white)(xxxxxxxxxxxx,.....x)sqrt90`

One way is to find pairs of number that multiply to `90` it is important though to be systematic so that you ensure you find them all.

`90=1xx90`

`90=2xx45`

`90=3xx30`

`90=5xx18`

`90=6xx15`

`90=9xx10`

`90=10xx9`

and the we repeat

so factors

`{1,2,3,5,6,9,10,15,18,30,45,90}`