Remainders

Let N = 1421 × 1423 × 1425. What is the remainder when N is divided by 12?

  1. 0
  2. 9
  3. 6
  4. 3

Answer

1421 = 118*12 + 5 = 12k + 5. where k = 118.

1423 = 12k + 7

1425 = 12k + 9

N = (12k + 5)(12 k + 7)(12k + 9)
 
When N is divided by 12, the remainder is same as the remainder, when 5 * 7 * 9 = 315 is divided by 12.

The correct option is D.