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What Is a Prime Number? (Mathematics Lesson)

What Is a Prime Number?

A prime number is a number that can be divided by only itself and one.

For example, 5 is a prime number. It can only be divided by 1 and 5.

The prime numbers are:

In a number square, the prime numbers are shaded below:

A prime number must be a whole number greater than 1, which is a natural number.

Because there is not limit to how big a natural number can be, we do not know all the prime numbers!

Quick Test

Here's a dynamic test on prime numbers.


Factors are numbers that you multiply together to get another number.

For example, the factors of 6 are 1, 2, 3 and 6, because:

1 × 6 = 6
2 × 3 = 6

For prime numbers, the only factors are 1 and the prime number itself.

The only factors of 5 are 1 and 5:

1 × 5 = 5


Any whole number that is not prime (called a composite number) can be broken down into a product of prime factors.

For example, 12 can be broken down into prime factors:

The fundamental theorem of arithmetic states that all natural numbers are either prime numbers or a product of prime numbers.