- Take a number greater than or equal to 2 and take its primes. e.g. 6 and its primes are 2 3 5
- calculate the factorial of its prime (nearest less) and calculate the sum from that number down to 1. e.g. 5! = 120 and sum 5 to 1 is 15
- As mod of the factorial of every number with 2 is zero, check the mod of the sum calculated with 10 e.g. mod of 15 with 10 is 5
- Divide factorial with the remainder (if possible). e.g. 120/5 = 24
Don't use builtin functions
primes
factorial
mod
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Test suit has been fixed, though the OP seems to miss the fact that people can still use rem().