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The greatest remainder when dividing by a number is always one less than that number. Therefore, for the divisors 3, 8, and 5, the greatest remainders would be 2 (for 3), 7 (for 8), and 4 (for 5). Among these, the largest remainder is 7, which corresponds to the divisor 8.

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6d ago

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Why should the remainder not be greater than the divisor?

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!


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