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Why is the remainder less than the divisor?
Because if the remainder is greater, then you could "fit" another divisor value into it. if they are equal, then you can divide it easily. Thus, the remainder is always lower than the divisor.
What is the greatest possible remainder if the divisor is 25?
24. It is always one less than the divisor.
What divisors give you a remainder of 24?
All divisors greater than 24, ie 25, 26, 27, ... can give a remainder of 24 when divided into something, as long as that something is 24 greater than a multiple of the divisor being used.The largest remainder any divisor can give is one less than the divisor itself - otherwise another chunk of the divisor can be removed and one added to the (integer part of the) quotient.
How big can a remainder be and why?
A remainder can be any non-negative number that is less than the divisor. If the remainder is bigger than the divisor, the divisor can go into it another one (or more) times until the remainder is brought into that range.
What is the largest remainder possible if the divisor is 63?
62. One less than the divisor.
