Question

How do you find all the factors of 44?

Answer 1

Find factor pairs.

`F_44= {1," "2," "4," "11," "22," "44}`

Explanation:

A factor is a number which divides into a bigger number without leaving a remainder. A number is always a factor of itself.

Factors are always in pairs. Dividing by one factor will give you the other.

To find all the factors of a number, start from 1 and consider all the possible factors up to the square root of the number.
(The square root lies in the middle of the factors arranged in order.)

`sqrt44 = 6. ....` The only numbers we need to consider are

`1," "2" "3" "4" "5" "6`

`1` is a factor: The factor pair is `color(blue)(1 xx44)`
`2` is a factor: The factor pair is `color(blue)(2xx22)`
`3` is not a factor of 44
`4` is a factor: The factor pair is `color(blue)(4xx11)`
`5` is not a factor of 44
`6` is not a factor of 44

The factors of 44 are therefore:

`color(blue)(1," "2," "4," "11," "22," "44)`
`color(white)(......................)color(red)(uarr)`
`color(white)(.....................)color(red)(sqrt44)`

Note that:

1 and the number itself are always factors of any number

Using a factor tree or prime factors in this case would not help, because they do not indicate all the possible combinations of the prime factors.