Question

What is the highest power of a number in a factorial?

Answer 1

To find the highest power of a prime number (x) in a factorial (N!),continuously divide N by x and add all the quotients.

Answer 2

To find the highest power of a number (N) in a factorial (F!), continuously divide F by N until the value of F is greater than power of n and then add all the quotients.

Let’s find the highest power of 5 in 100!

$\frac FN =\frac{100}{5}$ = 20  

$\frac{100}{5^2} =\frac{100}{25}$ = 4  

100/$5^3$ → here the denominator value is greater than numerator so let’s ignore the same.

20 + 4 = 24 is the highest power of 5 in 100!