PhDorBust said:The factorial of 1 trillion ends in many trailing zeros. Find the five digits that comes before the trailing zeros.
I know how to calculate the number of trailing zeros, but don't know what to do afterwards. This is a computational problem.
PhDorBust said:10^12, sorry.
Should it make a difference though?
The purpose of computing end-digits of large factorials is to determine the last few digits of a factorial number, which can be useful in a variety of mathematical and scientific applications. It can also help in understanding the patterns and properties of factorial numbers.
In general, any factorial number that has more than 100 digits is considered a large factorial number. However, the exact cutoff for what is considered "large" may vary depending on the specific application and computing capabilities.
The most efficient method for computing end-digits of large factorials is to use modular arithmetic. This involves taking the remainder of the factorial number when divided by a smaller number, such as 10, to determine the last digit(s).
Some potential challenges when computing end-digits of large factorials include the time and computing resources required, as well as the potential for overflow or underflow errors. Additionally, some factorial numbers may not follow predictable patterns, making it more difficult to determine the end-digits with accuracy.
Computing end-digits of large factorials can be used in cryptography, where large factorials are often used in encryption algorithms. It can also be used in statistical analysis and probability calculations, as well as in various scientific fields such as physics and chemistry where large numbers are often encountered.