# Is 43 a prime number?

Yes

A prime number is one that has as its factors only itself and 1. So for instance 3 is a prime number and 4 is not:

The quick answer is "no" and so 43 is prime.

The longer answer is that we can try to multiply numbers to get to 43:

43 is odd and so nothing times 2 will work

43 doesn't end in 0 or 5 so nothing times 5 will work

And there's no sense in continuing - if 2 times 23 is too big, nothing beyond this point will be smaller. And, in fact, we could have stopped much earlier because we already knew anything times 2, 3, 4, 5,... wouldn't work (I think technically the last attempt that was redundant was seeing that 5 was not a factor - but it was good to show definitively that these bigger numbers wouldn't work).

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Yes, 43 is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Since 43 has only two positive divisors, 1 and 43, it is prime.

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