# Difference Between Prime and Composite Numbers

Numbers form an integral part of mathematics as they help us in counting and measuring quantities. These numbers are classified as natural, real, complex, integers, rational, irrational, etc. Amongst the natural numbers are also the prime numbers and the **composite numbers**.

Mathematics is a subject that helps us to find and use patterns around us, hence enabling us to formulate new theories. Mathematical reasoning is useful in providing insight or predictions about nature. With the help of abstraction and logic, mathematics is developed from counting, calculation, measurement, and numbers hence play a vital role in mathematics. If one is good at number crunching, then mathematics no longer remains a riddle. Thus getting familiar with the types of numbers builds a basic foundational understanding of the course. Visit the Cuemath website to find some useful mathematical worksheets for practice on getting good at numbers.

The **prime numbers** are those natural numbers that are divisible by only themselves and by numeral one. In other words, their factors would be one and the number itself, making it a total of only two factors. While if the number is equal to any other natural numbers when multiplied, those numbers are composite numbers. Thus, composite numbers have more than two factors, or we can say a minimum of three factors. One thing to note is that number 1 is neither prime nor composite. A simple thing to remember is that the numbers that are not prime come under composite numbers.

## Let Us See Some Examples:

If we look at 2, factors of 2 are 1 and 2, and 2 is a prime number. 2 is an even number too, but it is not a composite number.

Let us look at 3, 3 has only two factors, i.e., it is divisible by only 1 and 3 itself. Hence 3 is a prime number.

Let’s take 4, factors of 4 are 1, 2, and 2, hence making it a composite number as it has a minimum of three numbers.

If we see 5, 222again it has only 1 and 5 as its factors, making it a prime number.

Let us see if 21 is prime or composite, if we factorize 21 we get 1, 3, 7, and 21 which means that 21 is a composite number.

A composite number is a positive integer that is formed when two positive integers are multiplied. Or it can be said that it is a positive integer that other than 1 and itself has at least one divisor. Every positive integer is composite, prime, or 1, so the composite numbers are in a way those numbers that are not prime and not numeral one.

To find out whether a number is a prime or a composite, we can do a divisibility test using the numbers 2, 3, 5, 7, 11, and 13.

Prime factorization of any given number can be done by breaking the number into its factors till all of its factors are prime numbers. For this proceed by dividing the given number from the smallest prime number and continue until all its factors are prime.

The smallest prime number that we know is 2. The other prime numbers being 3, 5, 7, 11, and 13. And interestingly, there is no largest prime number.

Prime numbers play a significant role in mathematics and in the field of computer science. As the long numbers are complex to deal with, and it is difficult to find the prime factors, such numbers are used for encryption and in creating secret codes, thus finding their utility in banks and creating encrypted codes for ATMs.