What is the remainder when 91x92x93x94x95x96x97x98x99 is divided by 1261?

The key to solving this question is knowledge of divisibility tests. We check 1261 with all prime numbers one by one. First hit is 13 (2, 3 & 5 can easily be ruled out. Then try 7 and 11).

Remaining number ie 1261/13 is 97.
1261 = 1 × 13 × 97

Now, 91 is divisible by 13 and 97 itself is present. So, 1261 will completely divide the expression.

Hence, the remainder = 0