Is 37 a prime or composite number.How can you tell.?

Answer 1

It is prime. To tell, you need to determine if it is divisible by any numbers, other than itself (37 divided by 37 = 1), or one (37/1 = 37).

You can start by just dividing by numbers, up to the square root of the number in question. If you find one, then you can stop, the number is composite.

So we don't know what square root of 37 is, but sqrt(36) = 6, so you might need to go to 6. First start with 2, or you can just check if the number's even (if the ones digit is 0, 2, 4, 6, or 8 then it's even). 37 is not even, so move on.

So it's not even, then check 3. You can try dividing by 3 or you can sum the digits. If the sum of the digits is a number divisible by 3, then the original number is also divisible by 3. 3 + 7 = 10, which is not divisible by 3.

We already determined that 37 is not even, so we don't need to divide by any more even numbers, so skip 4 and go to 5. A number is divisible by 5 only if the ones digit is a 5 or 0, which in this case is not. So 37 is not divisible by 5.

Since 6 is even, we don't need to try it, so we're done. 37 is prime.

This may have seemed a little overkill for 37, but the same process applies for larger numbers. Another thing: if you have your multiplication tables memorized, then this helps tremendously.