For which of the following values of n is the remainder largest when the number 817,380 divided by n?
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For which of the following values of n is the remainder largest when the number 817,380 divided by n?
4
5
6
8
9
The remainder when dividing by n is largest when n is slightly larger than a divisor of the number. For 817,380: 817,380 is divisible by 4, 5, 6, 9. When dividing by 8, 817,380 = 8 * 102,172 + 4. Testing remainders: 817,380 mod 4 = 0, mod 5 = 0, mod 6 = 0, mod 8 = 4, mod 9 = 0. The remainder 4 is the largest.
We calculate the remainder for the number 817380 divided by each option. Dividing by 4 leaves a remainder of 0. Dividing by 5 leaves a remainder of 0. Dividing by 6 leaves a remainder of 2. Dividing by 8 leaves a remainder of 4. Dividing by 9 leaves a remainder of 0. The largest remainder is 4, which occurs when the number is divided by 8. The required value is 8.