Question

Determine how many zeros are at the end of the number 132! show work and explanation.

Answer 1

do you know what the greatest integer function is?

Answer 2

no

Answer 3

the question boils down to how many factors of 5 are in 132, since there are more factors of 5 than of 2

Answer 4

every time a 5 is paired with a 2 you will get 10, so that will contribute to a zero at the end of the numbers
therefore solving this problem is the same as answering "how many factors of 5 are in 132!?"

Answer 5

i dont know how i would show my work though. do 132 divided by 5?

Answer 6

that is the first step
you get 26.4
ignore the .4, keep the 26
then divide by \(5^2=25\)

Answer 7

you get \(5.28\) ignore the .28, keep the 5

Answer 8

then divide by \(5^3=125\) you get 1 and some remainder, keep the 1

Answer 9

could yu show all the work at once please?

Answer 10

@robtobey will show it
maybe there is a snappier way, but i think that is basically what you have to do
then add up those numbers

Answer 11

ok thanks

Answer 12

32
30*3+2
Sorry, no sophistication here, just brute force.
Refer to the attachement.

Answer 13

but how would i explain there are 32 zeros

Answer 14

Refer to the attachment, the value of 132! calculated by Mathematica, and count them.

Answer 15

yea but i ahve to show work or explain why

Answer 16

\(26+5+1=32\)

Answer 17

hope it is clear how i got those numbers