Question

Write the Number Of Zeros In 100 Factorial?

Answer 1

Answer:

Each pair of 2 and 5 will cause a trailing zero. Since we have only 24 5's, we can only make 24 pairs of 2's and 5's thus the number of trailing zeros in 100 factorial is 24. 2.

Answer 2

To Find :

The Number of zero in 100 factorial

Factorial notation 

The notation n! represents the product of first n natural numbers, i.e., the product 1 × 2 × 3 × . . . × (n – 1) × n is denoted as n!. We read this symbol as ‘n factorial’. 

Thus, 1 × 2 × 3 × 4 . . . × (n – 1) × n = n !

For example,

1! = 1

2! = 1 x 2 = 2

3! = 1 x 2 x 3 = 6

4! = 1 x 2 x 3 x 4 = 24, which are the factors of the given number.

Solution:

100!

when we multiply 5 & 2 the answer of unit digit is zero. Clearly in 100! powers of 5 arise lesser than power of 2 .

We need is the number of times 5 & or power of 5 occurs, Which can be got by the above formula

The formula is given by,

n! =[ $\frac{n}{k}$] + [$\frac{n}{k^{2} }$] +.....∞

we write up to the power 2, Because 5³ = 125 which is greater than value of n.

n! = [ $\frac{100}{5}$ ] + [ $\frac{100}{25}$ ]

n! = 20+ 4

n! = 24  

The Number of Zero in 100! is 24