Question

The product of all integers from 1 to 100 will have the following numbers of zeros at the end ?

Answer 1

Generally, to find the number of trailing zeros in a product of integers we use the below formula

$\frac n5+\frac n{5^2} +\frac n{5^3}$+…  

The numerator should be greater than denominator in all cases in the above formula.

n is the integer for which the factorial needs to be identified.

n = 100

$\frac{100}{5} +\frac{100}{5^2}$ = No. of zeros

$5^3$= 125 which is greater than 0. Hence, we will add till $5^2$.

20 + 4 = 24  

Hence 24 zeros are available in the product of integers from 1 to 100.