IIT JEE , AIEEE Forum - Mathematics , Algebra

pathfinder

Hi

If you factorize 100! then number of zeros will occur when there is one (2 x 5 ) action is happening.
Now obviously in the factors of 100! powers of 5 will be much less then powers of 2.

so the number of zeros in 100! is :

powers of 5 + powers of ( 5 x 5) + powers of ( 5 x 5 x 5) + .... and so on

powers of 5                         = 100 / 5   = 20
powers of ( 5 x 5)                 = 20 / 5 = 4
powers of ( 5 x 5 x 5)            = 0 (as 4 is less then 5)

so the number of zeros are 24.

Cheers

Ask & Discuss Questions with Community & Experts