Question

How do you find all factors of 54?

Answer 1

The factors are:`" "1,2,3,6,9,18,27,54`

Explanation:

Find the square root first

`sqrt54~~ 7.35`

Half of the factors will be less than this.

Consider which numbers less than `7.35` are factors of `54`

`color(blue)(1,2,3),4,5,color(blue)(6),7`

use factor pairs to find the other factors which are bigger than `7.35`

`1 xx54, " "2xx 27` and so on..

`1,2,3,6,9,18,27,54` are all the factors

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Or write `54` as the product of its prime factors.

`54 = 2xx3xx3xx3`

Combine them in different ways:

One factor at a time: `" "1,2,3`
Two factors at a time:`" "2xx3 = 6;" "3xx3= 9`
three factors at a time:`" "2xx3xx3 = 18;" "3xx3xx3= 27`
all four factors:`" "2xx3xx3xx3 =54`

The factors are:`" "1,2,3,6,9,18,27,54`