Question

Given an integer n
Find if n! is divisible by 10
Where n! represents factorial of n

Answer 1

Answer:

Sum of first ‘n’ natural numbers: s = (n)*(n+1)/2 . This can be expressed as (n+1)!/2*(n-1)!

Now n!/s = 2*(n-1)!/(n+1).

From the above formula the observation is derived as:

If ‘n+1’ is prime then ‘n!’ is not divisible by sum of first ‘n’ natural numbers.

If ‘n+1’ is not prime then ‘n!’ is divisible by sum of first ‘n’ natural numbers.

Explanation:

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