Question

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

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

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.