How can you show that a number is prime or not?

Answer 1

To show that it's NOT prime, you have to find that in addition to '1' and itself, the number has another factor.

First, look for signs of obvious factors. The easy ones are 2, 3, 5, and 10.

-- If the number ends in 2, 4, 6, or 8, it's an even number, meaning 2 is a factor. It's not prime, and
you can stop right there.

-- If the sum of its digits is divisible by 3, then the whole number is divisible by 3. It's not prime, and you can stop.

-- If the number ends in 5, it's divisible by 5. It's not prime, and you can stop.

-- If the number ends in 0 (zero), it's divisible by 10. It's not prime, and you can stop.

If none of these pans out, then you have to slog through it the slow way. One after another, divide the
number by all the numbers from 2 up to half of the number. If any of the divisions comes out even, then the
number is not prime, and you don't have to try any more divisions.