Question

What is the greatest possible whole number remainder if you divide any number by 41?

Answer 1

The correct answer is:
40.

Explanation:
When we divide by 41, we are seeing how many times 41 will go into that number. If we had a remainder of 41 or larger, that means 41 would go into it again, which would change our answer. This means that 40 is the largest remainder we could possibly have.

Answer 2

The quotient remainder theorem: Given any integer A, and a positive integer B, there exist unique integers Q and R such that

A= B · Q + R where 0 ≤ R < B.

Q is called quotient and R is called remainder.

According to this theorem, when you divide any number by 41, you can obtain remainder R such that 0 ≤ R < 41. Then the greatest possible whole number remainder is 40.