How do you find all the factors of 44?

Find factor pairs.

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

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 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.