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Zeroes in a Factorial - Number Theory Video Lecture | Mathematics for NDA

FAQs on Zeroes in a Factorial - Number Theory Video Lecture - Mathematics for NDA

1. How many zeroes are there at the end of 100 factorial?

Ans. To find the number of zeroes at the end of 100 factorial, we need to determine the number of times 10 can be factored out of 100!. This can be done by dividing 100 by 5 (as each pair of 2 and 5 results in a zero at the end of a number), which gives us 20. Therefore, there are 20 zeroes at the end of 100!.

2. What is the formula to calculate the number of zeroes at the end of n factorial?

Ans. The formula to calculate the number of zeroes at the end of n factorial is to divide n by 5, then divide the result by 5, and so on, until the result is less than 5. The sum of all these divisions will give the number of zeroes at the end of n factorial.

3. Is it possible for a factorial to have zero zeroes at the end?

Ans. No, it is not possible for a factorial to have zero zeroes at the end since each pair of 2 and 5 results in a zero at the end of a number, and there are always more 2s than 5s in any factorial.

4. How can the number of zeroes at the end of a factorial be useful in real-life applications?

Ans. The number of zeroes at the end of a factorial can be useful in various fields such as computer science and mathematics for calculating large numbers efficiently, especially in algorithms and programming.

5. Can the number of zeroes at the end of a factorial be used to determine the highest power of a prime number in the factorial?

Ans. Yes, the number of zeroes at the end of a factorial can be used to determine the highest power of a prime number in the factorial since each pair of 2 and 5 contributes to the number of zeroes, which in turn determines the power of the prime number.

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Sep 10, 2025 Last updated

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