How can you work out prime numbers and composite numbers easily?

Answer 1

AnswerTo test if a number is prime or composite by hand, the easiest thing to do is test if it's divisible by numbers you know to be prime (start with 2, 3, 5, 7, and so on). If none of them divide it, once the numbers you're dividing by get bigger than the square root of the number you're testing (roughly - you don't need to waste time actually calculating the square root), you're done and know it's prime.

For example, here's how you'd test if 107 is prime:

It's odd, so it's not divisible by 2;

It's not divisible by 3 (use the divisibility rule: 1+0+7=8, not 3 or 6 or 9)

It's not divisible by 5 (doesn't end in 5 or 0)

It's not divisible by 7 (if it were, 107-7=100 would be divisible by 7, which we know isn't true)

At this point, we know it's prime, since we'd need to check 11 next. But 11*11=121, bigger than 107, so 11 is greater than the square root of 107.

For large numbers, the best thing to do is to use a computer.