Zeroes in a Factorial - Number Theory

# Zeroes in a Factorial - Number Theory Video Lecture | Quantitative Aptitude for SSC CGL

## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests

## FAQs on Zeroes in a Factorial - Number Theory Video Lecture - Quantitative Aptitude for SSC CGL

 1. What are zeroes in a factorial?
Ans. Zeroes in a factorial mean the number of trailing zeros present at the end of any factorial. For example, the factorial of 5 is 120, and it has one trailing zero. The factorial of 10 is 3628800, and it has two trailing zeros.
 2. How can we find the number of zeroes in a factorial?
Ans. To find the number of zeroes in a factorial, we need to count the number of factors of 5 in it. For example, the factorial of 10 has two factors of 5, so it has two trailing zeroes. Similarly, the factorial of 25 has six factors of 5, so it has six trailing zeroes.
 3. What is the highest power of 5 that can divide n! completely?
Ans. The highest power of 5 that can divide n! completely is given by the formula [n/5] + [n/25] + [n/125] + ...., where [] represents the floor function. For example, if n=25, then the highest power of 5 that can divide 25! completely is [25/5] + [25/25] = 5 + 1 = 6.
 4. Why is the number of factors of 5 important in finding zeroes in a factorial?
Ans. The number of factors of 5 is important in finding zeroes in a factorial because each factor of 5 contributes one trailing zero to the factorial. For example, the number 10 has one factor of 5 and two factors of 2, so it contributes one trailing zero to the factorial of 10.
 5. What is the significance of finding zeroes in a factorial?
Ans. Finding zeroes in a factorial is significant because it helps us to determine the number of times a number is divisible by 10. It is also useful in finding the highest power of a prime factor that can divide a factorial. Furthermore, it has applications in combinatorics, number theory, and probability.

## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests

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