Show that number N! can terminate in exactly 1,2,3,4,or 6 zeros but never 5 zeros?

Answer 1

A jar contains some red and some yellow jelly beans. If a child ate 1 red jelly bean, 1/7 of the remaining candies would be red. If instead the child ate 5 yellow jelly beans, 1/6 of the remaining candies would be red.

Answer 2

zeros at the end of n! come from factors that end in either 0 or 5

so the first zero shows up in 5!
e.g.
1!=1
2!=2
3!=6
4!=24
5!=120

that stays there until we reach 10! which is 3628800
punching in 15! in the Google search line gives
1 307 674 368 000
(after that it goes to scientific notation)

so critical values that cause more zeros are
20!, 25!, 30! etc.
let's look at 20!
20! = 1x2x3x4x5x6x7x8x9x10x11x12x13x14x15x16x17x18x19x20
the factors that cause zeros are
2x5x10x15x20 which is 30 000, so 20! ends in 0000

that will stay like that until 24! which still ends in 0000
but did you notice that all end with an even number before the last string of zeros,

Somebody has actually gone through the effort of printing out all results of the factorials from
1! to 1000! (believe it or not)
(Broken Link Removed)

look at the end of 24!
it looks like this 62.....360000
to get 25! we multiply that by 25
just consider the end result 36x25 or 900
so we are adding 2 zeros this time, and that "shows" it.

Answer 3

what is the answer to 1x2x3x4x5x6x7x8x9x10x11x12x13x14x15x16x17x18x19x20 please

Answer 4

1x23x4x5x66x7x8x9x10x11x12x13x14x15x16x17x18x19x20