What is the remainder when 85 × 87 × 89 × 91 × 95 × 96 is divided by 100?

Answer: (a) 0

85 and 95 each supply a factor 5, and 96 supplies several factors of 2, so the product contains 5 × 5 × 2 × 2 = 100. A multiple of 100 leaves remainder 0.

1. 85 = 5 × 17 and 95 = 5 × 19, which give 5 × 5 = 25.
2. 96 = 2⁵ × 3, which gives at least 2 × 2 = 4.
3. So the product has 25 × 4 = 100 as a factor; the remainder on division by 100 is 0.
4. Check: 85 × 96 × 95 = 775200, already ending in 00.

Remember · Before any remainder working, look for factors 2 and 5: enough of them make the product a multiple of 10 or 100.

Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error