Grades 11-12 Video Solutions 2010-11&12 Video Solutions 2010 problem20

11&12 Video Solutions 2010 problem20

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The task is to find the smallest prime divisor of the expression \( 10! + 1 \). By maximizing \( n \), we find that the largest possible value results from multiplication operations, leading to \( n = 10! + 1 \). The expression \( 10! \) is divisible by smaller primes like 2, 3, 5, and 7. However, \( 10! + 1 \) is not divisible by these primes, leaving 11 as the smallest prime divisor. Therefore, the smallest prime divisor of \( 10! + 1 \) is 11.

Keywords

smallest prime divisor

factorial

10!

prime numbers

mathematics