Let N be the greatest number that divides 1305, 4665, and 6905 leaving the same remainder in each case. What is the sum of the digits of N?

Concept / Approach

• If N leaves the same remainder on dividing several numbers, N must divide all pairwise differences.

Step-by-step calculation4665 − 1305 = 33606905 − 4665 = 22406905 − 1305 = 5600N = GCD(3360, 2240, 5600) = 1120Sum of digits of 1120 = 1 + 1 + 2 + 0 = 4

Final Answer4