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

  (UPSC CSAT – 2022)

1. 3
2. 2
3. 1
4. 0

Solution: (d)

1. Prime Factorization of the Divisor:
   • 1261 = 13×97
2. Check Factors in the Product:
   • The product 91×92×93×94×95×96×97×98×99 includes:
     • 91, which is divisible by 13 (91 = 13×7).
     • 97, which is directly present as a term in the product.
3. Conclusion:
   • Because both factors 13 and 97 (and thus 13×97 = 1261) divide the product completely, the remainder is 0