Prime Numbers and Composite Numbers

Prime Numbers

A prime number is a whole number that has exactly two factors, 1 and itself.

For example

The number 29 has exactly two factors, which are 1 and 29.

So, 29 is a prime number.

Some other examples of prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, ...

Composite Numbers

A number that has more than 2 factors is called a composite number.

For example:

The number 28 has six factors which are 1, 2, 4, 7, 14, and 28.

So, 28 is not a prime number. It is a composite numbers.

Example:

Determine whether each of the following number is prime.

a) 43

b) 57

Solution:

a) 43 is only divisible by 1 and 43. It is a prime number.

b) 57 ÷ 3 = 19. It is not a prime number.

The prime numbers up to 100 are

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

We can also use the Sieve of Eratosthenes to find out whether a number is prime or composite.

Is 1 a prime number?

No, the number 1 is not a prime number because it has only one factor (namely 1 itself),

Which number is the only even prime number?

The number 2 is the only prime that is even. All other even numbers have 2 as a factor and so they are composite numbers.

Twin primes are pairs of primes whose difference is 2.
(3, 5), (5, 7) and (11, 13) are examples of twin primes.

When two composite numbers have no common factors (other than 1), they are said to be relatively prime. For example, the numbers 8 and 15 are relatively prime.

The following video shows how to distinguish between prime numbers and composite numbers.

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