Find the largest number which divides 1305, 4665 and 6905 leaving same remainder in each case. Also, find the common Remainder.

Given that
x = 1305, y = 4665, z = 6905
Then ,
|x - y| = |1305 - 4665| = 3360
|y - z] = |4665 - 6905| = 2240
|z - x| =|6905 -1305| = 5600
∴ Required number = HCF of 3360, 2240 and 5600 = 1120
On dividing 1305 by 1120, remainder is 185.
On dividing 4665 by 1120, remainder is 185.
On dividing 6905 by 1120, remainder is 185.
∴ Common remainder = 185