The number of divisors of 2100 is _________.
(A) 42
(B) 36
(C) 78
(D) 72
Answer: (B)
Explanation:
2100 = 22 * 31 * 52 * 71 There are 3 choices for powers of 2, the choices are 0, 1, 2 Similarly, there are 2 choices for powers of 3, 3 choices for power of 5 and 2 choices for power of 7. So total number of divisors is 3 * 2 * 3 * 2 = 36