Question

how many zeroes will 50! end in?
a. 9
b 10
c 11
d 12

Answer 1

what do you mean "will 50"

Answer 2

see that 50!=3.0415 into 10^64

Answer 3

50!= 50 * 49 * 48 etc

Answer 4

@zaibali.qasmi what is that?

Answer 5

\(3.0415 \times 10^{64}\)

@sunshao1

Answer 6

how does that answer the question?

Answer 7

that is this which @geerky42 write here,..1

Answer 8

How many factors of 5: 10
How many factors of 5²: 2
How many factors of 2: so many...

So we have number of 0s at the end \(= 10+2 = 12\)

Answer 9

To put it in another view: \[50! = 50\times \ldots\times 45\times \ldots\times 40\times \ldots\times 30\times \ldots \times 25\times \ldots\\~~~~ = 2\cdot5^2\times \ldots\times 9\cdot5\times \ldots\times 8\cdot5\times \ldots\times 6\cdot5\times \ldots \times 5^2\times\ldots\]
So we can see that 50! contains 12 total of factors of 5, and clearly there are a lot of factors of 2, so we have \(5^{12}\cdot2^{12} = 10^{12}\), which put 12 0s to end.

Does this help?

Answer 10

kind of

Answer 11

ok i get the factors of 5, but where does the 5^2 come from and how does that add 2 so the answer is 12? cause i originally put 10

Answer 12

5^2 came from 50 and 25. so we have extra 2 5s