Question

What are the factors of 40?

Answer 1

The factors are `1`, `2`, `4`, `5`, `8`, `10`, `20`, `40`

Explanation:

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 square root 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`