Numbers/Counting

21! = 2¹⁸ × 3⁹ × 5⁴ × 7³ × 11 × 13 × 17 × 19

Total factors = 19*10*5*4*2*2*2*2

since first multiple in above equation that is 19 is all the powers of 2, and out of 19 only 1 that is 2⁰   is odd.

In all other cases it is even, hence resultant factor will be even. 

The only thing that affects the parity of factors are the powers of 2.

 Therefore the answer is 1/ 19.