Q: Number of even divisions of 504 is

(A) 12

(B) 24

(C) 6 ^{3}C_{2}

(D) 18

Sol. 504 = 2^{3} × 3^{2} ×7.. Any even divisor of 504 is of the form 2^{i} × 3i × 7k, where I ≤ i ≤ 3 , 0 ≤ j ≤2, 0 ≤ k ≤ 1. Thus total number of even divisors is

3 × 3 ×2 = 18

Hence (C), (D) are the correct answer.