How do you find all the factors of the number 45?

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Answer 1 · 2016-12-19T08:55:24

the factors of $" "45:{1,3,5,9,15,45}$

The best way would be to systematically find pairs of number that multiply to give 45

so $" "color(red)1xxcolor(red)(45)=45$

$45" "$ ends in a $5$ so $""5""$ must be a factor

$" "color(red)5xxcolor(red)(9)=45$

we can now use factors of the factors where possible

$9=3xx3" "$ we can use $3$

$" "color(red)3xxcolor(red)(15)=45$

$15$ has $" "3" "$ & $" "5" "$ which we have already used

any other combination gives a number greater than half of $" "45" "$ so we have found them all

so all the factors of $" "45:{1,3,5,9,15,45}$