20! has 4 zeros at its end whereas 25! has 6 zeros..
how come..
somebody help..
Hi hitesh091,
i'm assuming that you need to reason out only the increase in the no. of zeroes in 25! from the 4 zeroes in 20!
in order to find the 25! you'll have to multiply 20! with 21, 22, 23, 24 and 25, right?
consider the product 24x25 = 600, the two zeroes in this product will add to the already existing 4 zeroes of 20!. This leads to the increase of the number of zeroes from 4 to 6 when you compute 25!
hope it helped....
Every trailing zero in $\displaystyle n!$ results in the number of factors of fives in $\displaystyle n!$.
$\displaystyle 26!$ is divisible by $\displaystyle 5,~10,~15,~20,~\&~25=5^2$ that is six factors of five.
$\displaystyle 50!$ has 12 trailing zeros. Fifty is has 10 factors of 5 and 2 factors of 25.