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

- both 3 and 17
- both 7 and 13
- both 3 and 13
- both 17 and 7

**Answer**

55 + 17 = 72

Use formula

(x^{ }- y)^{3} = x^{3} - y^{3} - 3xy(x-y)

(72 - 17)^{3} = 72^{3} - 17^{3} - 3(72)(17)(72 - 17)

55^{3} + 17^{3} - 72^{3} = 3(72)(17)(55)

N is divisible by both 3 and 17.

**The correct option is A.**