Consecutive zeroes at the end of a number:
When we talk about consecutive zeroes at the end of a number, we are essentially looking for the number of factors of 10 in that number. This is because a factor of 10 represents a trailing zero at the end of a number.

Factors of 10:
To understand the factors of 10, let's break down the number 10 into its prime factors:
10 = 2 * 5

The prime factors of 10 are 2 and 5. In order to have a factor of 10, we need both 2 and 5 to be present in the prime factorization of a number.

Factors of 2 and 5:
Let's consider the prime factors of numbers from 1 to 10:
1 = 1
2 = 2
3 = 3
4 = 2 * 2
5 = 5
6 = 2 * 3
7 = 7
8 = 2 * 2 * 2
9 = 3 * 3
10 = 2 * 5

From the above list, we can observe that the number of factors of 2 is more than the number of factors of 5. Therefore, the number of factors of 10 will be limited by the number of factors of 5.

Calculating the factors of 5 in a number:
To find the number of factors of 5 in a number, we divide the number by 5 and count the number of whole numbers obtained. For example, in the range from 1 to 10, the number of factors of 5 is 1 (from 5 itself).

Calculating the factors of 10 in a number:
To find the number of factors of 10 in a number, we divide the number by 10 and count the number of whole numbers obtained. For example, in the range from 1 to 10, the number of factors of 10 is 0 (as there are no whole numbers obtained).

Calculating the factors of 5 and 10 in 100!:
In 100!, the number of factors of 5 will be determined by dividing 100 by 5 and counting the number of whole numbers obtained. Similarly, the number of factors of 10 will be determined by dividing 100 by 10 and counting the number of whole numbers obtained.

To calculate the number of factors of 5 and 10 in 100!, we can follow these steps:

1. Divide 100 by 5: 100 ÷ 5 = 20
2. Divide 100 by 10: 100 ÷ 10 = 10

Therefore, there are 20 factors of 5 and 10 factors of 10 in 100!.

Calculating the factors of 5 and 10 in 200!:
Similarly, in 200!, the number of factors of 5 will be determined by dividing 200 by 5 and counting the number of whole numbers obtained. The number of factors of 10 will be determined by dividing 200 by 10 and counting the number of whole numbers obtained.

To calculate the number of factors of 5 and 10 in 200!, we can follow these steps:

1. Divide 200 by 5