Despite my distaste for decimal digits, I noticed (while showing Mathematica to new user Miles) that 52! ends in twelve 0s both in decimal and hex. Equality happens for Select[Range[0, 101], IntegerExponent[#!, 10] == IntegerExponent[#!, 16] &] {0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 20, 21, 22, 23, 28, 29, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 65, 70, 71, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 90, 91, 95, 100, 101} with gradually declining frequency: In[535]:= Count[Range@99999, n_ /; IntegerExponent[#, 10] == IntegerExponent[#, 16] &[n!]] // tim During evaluation of In[535]:= 3610.464197,0 Out[535]= 23617 Is the asymptotic density finite? --rwg