## Difference Between Prime and Composite Numbers

**Prime vs Composite Numbers**

In math, some terms often confuse the students; a good example of this is the difference between “prime numbers” and “composite numbers.” It can be quite complicated to some, but actually, it is really simple. It all relates to the concept of natural numbers and their factors which we all know about. Readers will be clarified with terms as soon as they reach the end of this article.

*Prime numbers*

In natural numbers, which are one to infinity, that is, [1, 2, 3, 4, 5… infinity]; those numbers which can have only two factors, one is the number 1 and the other is the number itself, are called prime numbers. Simply put, those numbers which can be divided only by 1 and themselves are called prime numbers. So they only have two divisors.

For example:

3 (factors are 1 and 3);

7 (factors are 1 and 7), etc.

So if counted, prime numbers are infinity.

[2, 3, 5, 7, 11, 13, 17, 19… infinity]

Prime numbers are always odd numbers, except 2, because if they were even, they would have been divisible by 2 which is not a property of prime numbers.

*Composite numbers*

All the numbers other than prime numbers, except 1, are composite numbers because they have more than two factors. That is, composite numbers can be divided by 1, themselves, and some other numbers also.

For example:

4 (factors are 1, 2 and 4);

20 (factors are 1, 2, 5 and 20), etc.

Here also, we have infinite composite numbers.

[2, 4, 6, 8, 9, 10, 12, 14, 15… infinity]

Composite numbers can be even or odd depending upon the factors they have. If it has a minimum of one even number, it will be an even number. If it has no even number in its factors, then it will be an odd number.

The number 1 in natural numbers is an exception as this number cannot be categorized as a prime or composite number.

Summary:

1.Prime numbers have 1 and themselves as their factor while composite numbers can have more factors than 1 and themselves.

2.Smallest prime number is 2.

3.Smallest composite number is also 2.

4.The number 1 is neither a prime number nor a composite number.

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