Question

A number has exactly eight factors. Two of the factors are 8 and 20. What are all the factors of the number?

Answer 1

1, 2, 4, 5, 8, 10, 20, and 40

Explanation:

If 8 is a factor, then so are 2 and 4.

If 20 is a factor, then so are 5 and 10.

1 must be a factor by default.

So the 8 factors are:

1, 2, 4, 5, 8, 10, 20, ??

Factors come in pairs, and their products always add up to the number itself, which is a factor. The pairs are the first and last, second and second last, etc.

In this case, all the pairs multiply to 40:

`5 xx 8 = 40`
`4 xx 10 = 40`
`2 xx 20 = 40`

So the last factor must be 40 (the number in question itself).

Final Answer