What is the remainder when 91 × 92 × 93 × 94 × 95 × 96 × 97 × 98 × 99 is divided by 1261?

Answer: (d) 0

1261 = 13 × 97. The product contains 91 = 7 × 13 and also 97, so it is a multiple of 1261 and the remainder is 0.

1. Factorise the divisor: 1261 = 13 × 97.
2. The product contains 91 = 7 × 13 and the factor 97.
3. So the product is a multiple of 13 × 97 = 1261, and the remainder is 0.

Remember · Before dividing a big product, factorise the divisor and look for its factors inside the product.

Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error