Question

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

Answer 1

4

Explanation:

You want the sum of digits of the largest number that divides 1305, 4665, and 6905 with the same remainder.

Largest divisor

We can look at 4665/1305 ≈ 3.57 and 6905/1305 ≈ 5.29 for a clue as to the divisor of interest. These quotients tell us that one possibility is the value that would give quotients of 4 and 6 after the remainder is subtracted from each of the numbers.

For 1305 and 4665, if r is the remainder, we require ...

4(1305 -r) = 4665 -r

5220 -4665 = 4r -r

555/3 = r = 185

If 185 is the remainder in this scenario, then 1305 -185 = 1120 is the divisor. Checking the remainder with 6905, we find ...

6905/1120 = 6 r 185

Sum of digits

The sum of digits of this divisor is 1 + 1 + 2 + 0 = 4.

The sum of the digits in N is 4.