By factoring them. Prime numbers have only two factors. Composite numbers have three or more.
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You first find all of the factors of the number. A Prime number has only 2 factors which are 1 and itself. Composite numbers are everything else except 1 and 0.
The product of two prime numbers will be composite.
Products of prime numbers are composite numbers.
The opposite of prime numbers are composite numbers.
Composite numbers have more than two factors. So, the numbers which have two or less than two factors are not composite numbers. Numbers which have exactly two factors are prime numbers. 1 is an exceptional case because it is neither prime nor composite since it has only one factor which is 1.
All numbers that only have one and itself as factors are prime. Therefore, to tell if a number is prime simply find it's factors. If it has more than two factors than it is not a prime number, otherwise it is composite.