Why should the remainder not be greater than the divisor?

Answer 1

It must be less else you have not divided properly; you could divide again 1 or more times!

If the remainder is equal to the divisor (or equal to a multiple of the divisor) then you could divide again exactly without remainder. If the remainder is greater but not a multiple of the divisor you could divide again resulting in another remainder.

E.g. Consider 9/2. This is 4 remainder 1. Let's say our answer was 3 remainder 3; as our remainder "3" is greater than the divisor "2" we can divide again so we have not carried out our original division correctly!

Answer 2

Because if the remainder was larger than the divisor, then the divisor could go into the dividend again.