- #1
murshid_islam
- 457
- 19
how can i find the number of zeroes at the end of 100!
how can i find the number of zeroes at the end of n!
thanks in advance.
how can i find the number of zeroes at the end of n!
thanks in advance.
murshid_islam said:how can i find the number of zeroes at the end of 100!
how can i find the number of zeroes at the end of n!
thanks in advance.
You are WRONG, SteveRives.SteveRives said:Your question is the same as finding out how often 5 is a prime factor on the natural numbers.
So I am guessing that 100! has 20 zeros, because in counting by fives, we get to 100 after 20 steps.
A factorial is a mathematical operation in which a number is multiplied by all the numbers below it. For example, the factorial of 5 (written as 5!) is equal to 5 x 4 x 3 x 2 x 1 = 120.
Zeroes appear at the end of a factorial because the numbers in the multiplication sequence include factors of 5 and 2. When these factors are multiplied together, they result in a zero at the end of the number.
The number of zeroes at the end of a factorial can be determined by counting the number of multiples of 5 in the factorial's number. For example, in 10!, there is one multiple of 5 (5), which means there is one zero at the end of the number. In 25!, there are two multiples of 5 (5 and 25), which means there are two zeroes at the end of the number.
Yes, there is a limit to the number of zeroes at the end of a factorial. The maximum number of zeroes at the end of a factorial is equal to the number of multiples of 5 in the factorial's number. For example, in 120!, there are six multiples of 5 (5, 10, 15, 20, 25, and 30), so there can be a maximum of six zeroes at the end of the number.
To write a factorial without any zeroes at the end, you can rearrange the numbers in the multiplication sequence to ensure that there are no factors of 5 or 2. For example, instead of writing 10! as 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1, you can write it as 10 x 9 x 8 x 7 x 6 x 3 x 4 x 2 x 5 x 1. This will result in a factorial with no zeroes at the end.