Written in base six, how many zeros does 20! end with?

A trailing zero in base six needs a factor $6=2\times 3$, so count both primes inside 20!. Threes: ⌊20/3⌋ + ⌊20/9⌋ = 6 + 2 = 8. Twos: ⌊20/2⌋ + ⌊20/4⌋ + ⌊20/8⌋ + ⌊20/16⌋ = 10 + 5 + 2 + 1 = 18. Each 6 uses one of each, so the number of zeros is the smaller count, 8 — dividing 20! by 6 eight times in a row leaves a whole number, a ninth time does not. The trap is 4: that is how many zeros 20! ends with in base TEN, where the scarce prime is 5 rather than 3. Stopping at ⌊20/3⌋ gives 6.