What is the remainder when $85 \times 87 \times 89 \times 91 \times 95 \times 96$ is divided by 100?
What is the remainder when $85 \times 87 \times 89 \times 91 \times 95 \times 96$ is divided by 100?
0
1
2
4
Solution
The product contains 95 and 85, each contributing a factor of 5, giving $5^2 = 25$. It also contains $96 = 2^5 \times 3$, contributing $2^2 = 4$. Together $25 \times 4 = 100$ divides the product. Hence the remainder when divided by 100 is 0.