Question

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

Solution:
N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
= H.C.F. of 3360, 2240 and 5600 = 1120.
Sum of digits in N = (1 + 1 + 2 + 0) = 4

Aren't we supposed to find the HCF (1305, 4665, 6905) rather than that of the HCF(4665 - 1305), (6905 - 4665) and (6905 - 1305)?

Answer 1

Dear student we will find the HCF of number if we have to find the largest number which will divide the number completely.In that case remainder will be zero or we will not get remainder because HCF will completely divide all numbers.
But in this we have to find the greatest number which will leave the remainder and all numbers must leave same remainder so we have to take difference between numbers which will give same remainder in all three cases.