We know (and if not prove it!) that the maximal power of a prime dividing is given by , where is the floor function = the greatest integer that is less than or equal .

Note that the above sum is finite since

So the maximal power of 2 dividing 100! is , and the max. power of 2 dividing 32! is , and the one

dividing 68 is , thus the number is odd.

Tonio