What is the remainder when 91x92x93x94x95x96x97x98x99 is divided by 1261?
What is the remainder when 91x92x93x94x95x96x97x98x99 is divided by 1261?
3
2
1
0
Solution
$1261 = 13 \times 97$. The product $91 \times 92 \times \cdots \times 99$ contains $91 = 13 \times 7$ (a multiple of 13) and $97$ itself. So the product is divisible by both 13 and 97, hence by 1261. The remainder is 0.