20! = 20 * 19 * … 10 * 9 *… 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 that’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 … . 12 . 11 . 9 . 8 … . 2 . 1
(20! + 11) = 11(y + 1)
where y = 20 . 19 . 18 . 17 … . 12 . 10 . 9 . 8 … . 2 . 1
(20! + 13) = 13(z + 1)
where z = 20 . 19 . 18 . 17 … 14 . 12 . 11 . 9 . 8 … . 2 . 1
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So if it’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, that’s exactly what this question is testing!
So how can we identify if a number is prime? Im confused…
Check out “Is it Prime?” 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 isn’t part of 20!
Yeah, 20! + 23 would be prime, but it’s not one of the answer choices