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##