trailing numbers

[francoisph]

How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?

[Rich@VeritasPrep]

What they're really asking is:

How many factors of 10 are there in 25!. A factor of 10 corresponds to an extra zero.

10 is equal to 2 times 5, so we need both a factor of 2 and a factor of 5 to create a factor of 10.

You're multiplying 25*24*23* ... *3*2*1.

Of the numbers, only 25, 20, 15, 10, and 5 have a factor of 5, and there are two factors of 5 in 25. That's a total of 6 factors of 5.

There are obviously many more factors of 2, but you can only get 6 factors of 10.

There will be 6 trailing zeros.

[francoisph]

you missed 25=5^2

answer will be 6 I think

[jube]

No. of 0s depend on the no. of 10s in 25!
No. of 10s depend on no. of 2s & 5s.

So 25! has:
No. of 2s - 17
No. of 5s- 6

Therefore no. of 10s will be 6 (since 5 is just 6). Therefore, 25! will have 6 zeroes after the rightmost non-zero digit

[mj78ind]

How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?

Any combination of 5 and 2 AND 10 will give one trailing zero:

5 X even # (from the 5 in 25!)
10
3 X 5 X even # (from the 15 in 25!)
20
5 X even # AND 5 X even # (Note: 25 will give 2 trailing zeros and not one, one for each 5 in 25)

Hence a total of 6 trailing zeros.

[Rich@VeritasPrep]

Indeed I did miss 5^2 = 25. Nice catch!

Correcting my previous post now

[amising6]

How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?

for zero you need to find number of 5 and 0

now to find number of 5 in 25!



here goes the formula 25/5 you get 5 quiotent
then you divide quiotent 5 by 5 you get 1
which is not furthur divided so number of 5 will be 5+1=6

similairly no of 2 in 25 !
25/2 you get 12 ,12 divided by 2=6 when 6 divided by 2 you get 3 when 3 divided by 2 you get 1
so number of 2 's (add all the quotient dont worry about remainder) 12+6+3+1=22 two's

now there are 6 5's along with 6 2's will give 6 trailing zeroes