Question

What has the same quotient and remainder as 138 divided by 42 and 63 divided by 17?

Answer 1

138 divided by 42 gives 3 with remainder 12.

63 divided by 17 also gives 3 with remainder 12.

So, we need to build another division that gives gives 3 with remainder 12.

If we want a remainder of 12, we must divide by at least 13 (the remainder can't be greater than what you're dividing for).

Since

`13*3+12 = 39+12=51`

We have that 51 divided by 13 gives 3 with remainder 12.

In general, pick any number k>12 and define

`n=3k+12`

And you will be sure that n divided by k gives 3 with remainder 12.