The numbers 11284 and 7655 when divided by a number of three digit, leave the same remainder. Find the number of three digits.

Let the remainder in each case be t. Then, (11284 – t) and (7655 – t) are exactly divisible by that three digit number. Hence, their difference is [(11284 – t ) – (7655 – t ] = 3629 will also be exactly divisible by that three digit number. In other words that divisor will be a factor of 3629. Now, 3629 = 19 ×191 Since both 19 and 191 are prime numbers, the three digit number is 191. Hence, the required number = 191