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).
