20! = 20 * 19 * â€¦ 10 * 9 *â€¦ 3 * 2 * 1

So we know 10 is a factor of 20!

So, we can write the first answer choice like this:

10( 20!/10 + 1)

So the first value is definitely not prime.

Can you try and apply this to the others?

How do we know this is not a prime? is it because the final value will be multiplied by 10?

10( 20!/10 + 1)

@phobia851 thatâ€™s right, in each of the above, we can take the number that is being added as a common out of the bracket, and since it is being multiplied so is a factor.

(20! + 10) = 10(x + 1)

where x = 20 . 19 . 18 . 17 â€¦ . 12 . 11 . 9 . 8 â€¦ . 2 . 1

(20! + 11) = 11(y + 1)

where y = 20 . 19 . 18 . 17 â€¦ . 12 . 10 . 9 . 8 â€¦ . 2 . 1

(20! + 13) = 13(z + 1)

where z = 20 . 19 . 18 . 17 â€¦ 14 . 12 . 11 . 9 . 8 â€¦ . 2 . 1

So if itâ€™s a prime number greater than the factorial given, would it be a prime in that case? for e.g. would these be primes:

20! + 23 or 20! + 29

Nope, thatâ€™s exactly what this question is testing!

So how can we identify if a number is prime? Im confusedâ€¦

Check out â€śIs it Prime?â€ť on PrepSwift

Thanks, what if we get a number in the form of a factorial similar to the question above and we are asked if these numbers are primes? how would we do that ?

Only 2! is prime.

Everything else is a bunch of integers multiplied together, right?

why would 20! + 23 not be a prime though? 23 isnâ€™t part of 20!

Yeah, 20! + 23 would be prime, but itâ€™s not one of the answer choices