Highly selective Backlog Qs for JEE MainMathematicsPermutation and Combination
For N = 12600 , the number of even divisors is
Options
- A72
- B54
- C18
- DNone of these
Correct answer
B. 54
Step-by-step solution
On prime factorization we have, N = 12600 = 2 3 3 2 5 2 7 1 . Number of factors = 3 + 1 2 + 1 2 + 1 1 + 1 = 72 . Removing power of 2 remaining factors which are odd = 2 + 1 2 + 1 1 + 1 = 18 . ∴ Even factors = 72 - 18 = 54 . Hence, the answer is 54 .