For which n is the remainder largest when the number 817,380 is divided by n?

(A) 4

(B) 5

(C) 6

(D) 8

(E) 9

7380 is divisible by 5 because it ends in 0.

It is divisible by 2 because it is even and by 4 because 80 is divisible by 4.

However, it is not divisible by 8 because 380 isn’t.

The sum of its digits is 27, which is divisible by 3 and by 9.

Because it is divisible by both 2 and 3, it is also divisible by 6.

817,380 is divisible by all the numbers in the list except 8.

Hence, 8 must give the largest remainder because it is the only one that is not zero.

The correct answer is (D).

(A) 4

(B) 5

(C) 6

(D) 8

(E) 9

7380 is divisible by 5 because it ends in 0.

It is divisible by 2 because it is even and by 4 because 80 is divisible by 4.

However, it is not divisible by 8 because 380 isn’t.

The sum of its digits is 27, which is divisible by 3 and by 9.

Because it is divisible by both 2 and 3, it is also divisible by 6.

817,380 is divisible by all the numbers in the list except 8.

Hence, 8 must give the largest remainder because it is the only one that is not zero.

The correct answer is (D).