CSAT 2024 Solutions - 421 and 427, when divided by the same number, leave the same remainder 1. How many numbers can be used as the divisor in order to get the same remainder 1 ?

‍

A. 1

B. 2

C. 3

D. 4

‍

Answer: C

‍

‍

We are given the numbers 421 and 427. Subtracting 1 from both, we get 420 and 426.

‍

Step 1: Find the prime factors:

‍

- 420 = 2 × 2 × 3 × 5 × 7

- 426 = 2 × 3 × 71

‍

Step 2: Determine common factors:

The common factors between 420 and 426 are 2 and 3, and their multiple, 6.

‍

Therefore, the divisors that can give the same remainder 1 are 2, 3, and 6, resulting in 3 possible divisors.

‍