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.