The greatest remainder when dividing by 5 is 4. This is because when a number is divided by 5, the possible remainders are 0, 1, 2, 3, and 4. Since 4 is the highest value in this set, it is the greatest remainder one can obtain when using 5 as the divisor.
7
The greatest integer remainder is 7 but otherwise, 7.999... .
62
7
24. It is always one less than the divisor.
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.
44
7
The divisor is 9. quotient x divisor + remainder = dividend ⇒ quotient x divisor = dividend - remainder ⇒ divisor = (dividend - remainder) ÷ quotient = (53 - 8) ÷ 5 = 45 ÷ 5 = 9
The greatest integer remainder is 7 but otherwise, 7.999... .
37
62
75
7
24. It is always one less than the divisor.
When dividing by 3, the possible remainders are 0, 1, or 2. Therefore, the greatest remainder when the divisor is 3 is 2. This means that any integer can yield a remainder of up to 2 when divided by 3.
12-1, that is, 11.