terminal zeroes

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how would you figure out how many terminal zeroes are at the end of 1x2x3x4x5x6x7x8x9x10x11x12x13x14x15x16x17x18x19x20 WIThOUT using a calculator?
With a lot of time I think.

on a calc it is just 20! = 2.4390200817664 x 10^18

so that has 4 terminal zeros.

You taught me a new term - I had never heard of terminal zeros before.

1x2x3x4x5x6x7x8x9x10x11x12x13x14x15x16x17x18x19x20

this question is driving me crazy

19*18 ends it a 2 (9*8=72) I'll come back to 20
so 19*18*17 ends with a 4 (2*7=14)
so 19*18*17*16 ends with a (4*6=24) 4
so 19*18*17*16*14 ends with a (4*4=16) 6 I'll come back to 15
so 19*18*17*16*14*13 ends with a (6*3=18) 8
so 19*18*17*16*14*13*12 ends with a(8*2=16) 6
so 19*18*17*16*14*13*12*11 ends with a (6*1=6) 6
9*8=72
so 19*18*17*16*14*13*12*11*72 ends with (6*2=12) 2 I'll come back to 10
7*6=42
so 19*18*17*16*14*13*12*11*9*8*42 ends with(2*2=4) 4 I'll come back to 5
4*3*2*1 = 24
so 19*18*17*16*14*13*12*11*9*8*24 ends with (4*4=16) 6
Now we haven’t done
5*15*10*20 = 5*20*10*15=15000
So we have at least 3 zeros
5*6=30 so there is the 4th zero.

This is really clutsy - there must be a better way of doing it.

By the way, there is only one 'e' in zeros.