Question

let n be the greatest number that will divide 1305;4665;6905 leaving the same remainder in each case the sum of the digits of n is.


one who give the correct answer will marked as brienliest.....don't cheat give me full solution of this question

Answer 1

Since the remainder is same in each case, we will use the following formula- 
H.C.F (x, y, z)= H.C.F of (x -y), (y- z), ( z-x)

So, let's take out the H.C.F of 1305, 4665 and 6905 (leaving the same remainder)

= H.C.F of (4665 - 1305), ( 6905- 4665) and ( 6905- 1305) 
=H.c.f of 3360, 2240 and 5600 which is = 1120.

Sum of digits of 1120= (1+1+2+0)= 4.
Answer = 4.