Math Basics

More About Numbers

What are prime and composite numbers?

There are many definitions of prime numbers—and they all mean the same thing in translation. For example, prime numbers are defined as positive integers (natural numbers) that are greater than 1 and have only 1 and the prime number as divisors (factors). Another definition is an integer greater than 1, in which its only positive divisors are 1 and itself. Still yet another definition is that a prime is a natural number that has exactly two distinct natural number divisors, 1 and itself. For instance, the prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, and 19. All other integers greater than 1 that are not prime numbers are called composite numbers.

There are other rules concerning prime and composite numbers. The number 1 is unique, and is not considered a prime or composite number. And one of the basic theorems of arithmetic is that any positive integer is either a prime or the product of a unique set of prime numbers. For example, the number 12 is not a prime, but it has a unique “prime calculation” written as: 2 × 2 × 3.


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