Prime and Composite Numbers

Prime Numbers

Prime numbers are a very special type of counting number (natural number). To be a prime number, the number must have exactly two distinct counting number (natural number) factors

Example: The value seven, 7, is a prime number because the only counting number factors are 1 and 7. That is, 7 · 1 = 7 and there is no other pair of counting numbers that when multiplied give a product of 7.

Example: The value six, 6, is not a prime number because 1, 2, 3, and 6 are all counting number factors of six. That is, 1 · 6 = 6 and 2 · 3 = 6. Since six has four factors, six cannot be a prime number.

Example: The value one, 1, is not a prime number because the only counting number factor of one is one. That is, 1 · 1 = 1 is the only product of counting numbers to result in one. Since the definition of a prime number required exactly two distinct counting number factors, one cannot be a prime number.

Note that definition of a prime number excludes the possibility that 1 is a prime. For this reason, many people state that a prime number must be greater than 1 and its only counting number factors are itself and 1.

Definition of Prime and Composite Numbers:

We say that a natural number, p > 1, is prime if its only natural number factors are p and 1. If a natural number is not prime, then we say that it is composite.

Self-Check Problem

List the first five prime numbers.

Solution

return to top | previous page | next page