## Task 4 - 060514

We are looking for a natural number with the following properties:

If you divide 100 by this number, the remainder is 4, and if you divide 90 by this number, the remainder is 18.

What is the number we are looking for?
Let $a$ be the number we are looking for. If 100 leaves a remainder when divided by $a$, then $100-4=96$ is a multiple of $a$. Similarly, $90-18=72$ must also be a multiple of $a$. $a$ must also be greater than 18, otherwise a remainder of 18 could not occur.

72 and 96 have only one common divisor that is greater than 18. This divisor is 24, so the sought $a$ is 24.