The store clerk has 21 mugs to display on shelves. She wants to display an equal number of mugs on each shelf with no mugs left over. Which problem below shows a way she can do this?

The concept to do this question is to break the number into its factors and then make different combination.

The given number has just two factors

The factors of 21 are 3 & 7.

Which means

21 = 3 * 7.

So

Either we can have 7 shelves with 3 mugs on each shelf.

Or

We can have 3 shelves with 7 mugs on each shelf.

This way as 21 is divisible by 3 & 7. No mugs shall be left out.

So We have two solutions to this.

7 shelves with 3 mugs on each shelf.

3 shelves with 7 mugs on each shelf.