# What are the factors of 40?

The factors are ##1##, ##2##, ##4##, ##5##, ##8##, ##10##, ##20##, ##40##
I find factors in pairs, It will look like more work than it is, because I will explain how I am doing these steps. I do most of the work without writing it down. I’ll put the explanation in black in [brackets] and the answer in ##color(blue)”blue”##.
I’ll proceed by starting with ##1## on the left and checking each number in order until either I get to a number already on the right or I get to a number greater than the of 40.
##color(blue)(1 xx 40)##
[I see that 40 is divisible by 2, and do the division to get the next pair]
##color(blue)(2 xx 20)##
[Now we check 3. But 40 is not divisible by 3. I usually write a number before I check, so if a number is not a factor, I cross it out.]]
##color(blue)cancel(3)##
[Now we need to check 4. Up above, we got ##40 = 2xx20## since ##20 = 2xx10##, we see that ##40 = 2xx2xx10 = 4xx10##]
##color(blue)(4 xx 10)##
[The next number to check is 5. We can either divide ##40 -: 5## to get ##8## or split up the ##10## in the last factor pair: ##40 = 4xx10 = 4xx2xx5=8xx5##]
##color(blue)(5xx8)##
{Move on to 6. But 40 is not divisible by 6. — 6 is not a factor of 40.
##color(blue)cancel(6)##
[40 is not divisible by 7.]
##color(blue)cancel(7)##
The next number, ##8##, already appears on the list above (on the right).
For numbers greater than ##8## to be factors of ##40## they would have to be multiplied by something less than the ##5## we use in ##8xx5=40##. We’ve already checked the smaller numbers, so we’re done.
The factors are ##1##, ##2##, ##4##, ##5##, ##8##, ##10##, ##20##, ##40##

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