wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find the highest power of 5 dividing 100! and find number of zero at the end of 100!

Open in App
Solution

Highest exponent of a prime number a in n! is
=[na]+[na2]+[na3]+....
where [.] is greatest integer formation
Exponent of 5 in 100!
is =[1005]+[10052]+[10053]+....
=20+4+0+0....
=24
To make a zero in the end, use need a 10 as a factor
i.e., a product of 2 and 5
Exponent of 2 in 100! will be more than that of 5, as 2 is smaller number.
Hence 524 will multiply with 224 to make 1024
24 zeroes are there at the end of 100!

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Permutations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon