Is the number 437 prime or composite?

Answer 1

In general it's hard to know. You have to keep trying to divide by prime numbers to see if they go evenly. 437 is odd, so it's not divisible by 2. The next test is divisibility by 3, and the trick is to add the digits: 4+3+7 = 14. Since 14 isn't divisible by 3 then neither is 437. Clearly 5 doesn't work either.

I can do 7, 11, 13 in my head to see they don't divide. How high do you have to go trying primes? No higher than square root 437, which would be in the low 20s because 20^2=400. So all that's left are 17 & 19, since 23 is already too big. 17 & 19 don't work, either, so 437 is prime.