Let N = 55^3 + 17^3 - 72^3. N is divisible by

Divisibility

Let N = 553 + 173 - 723. N is divisible by

  1. both 3 and 17
  2. both 7 and 13
  3. both 3 and 13
  4. both 17 and 7

Answer

55 + 17 = 72

Use formula

(x - y)3 = x3 - y3 - 3xy(x-y)

(72 - 17)3 = 723 - 173 - 3(72)(17)(72 - 17)

553 + 173 - 723 = 3(72)(17)(55)

N is divisible by both 3 and 17.

The correct option is A.