If you have n! in binary, count the number of zeros at the end of its binary expansion and call this count k. The number k+1 approximates n relatively closely

If you have n! in binary, count the number of zeros at the end of its binary expansion and call this count k. The number k+1 approximates n relatively closely (the error n-k is the number of ones in n's binary expansion—see http://www.cut-the-knot.org/blue/LegendresTheorem.shtml http://www.cut-the-knot.org/blue/LegendresTheorem.shtml).