Question

let n be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. find the sum of the digits in N

Answer 1

If the remainder is same in each case and remainder is not given, HCF of the differences of the numbers is the required greatest number

6905 - 1305 = 5600

6905 - 4665 = 2240

4665 - 1305 = 3360

Hence, the greatest number which divides 1305, 4665 and 6905 and gives the same remainder, N

= HCF of 5600, 2240, 3360

= 1120

Sum of digits in N

= Sum of digits in 1120

= 1 + 1 + 2 + 0

= 4