Primes and Composites

What is a Prime Number?

A prime number is a whole number greater than $$1 that only has exactly $$2 distinct factors, $$1 and itself. For example, $$3 is a prime number, since $$3=1×3=3×1 and this is the only way we can write $$3 as the product of two whole numbers. Similarly, $$7=1×7 and $$31=1×31, so $$7 and $$31 are also prime numbers.

A common misconception is that $$1 is a prime number. Thinking back to the definition, that a prime number has exactly two distinct factors, we can see that $$1 can only be written as a product of two numbers in the form $$1×1. Since these two numbers are the same (not distinct), then $$1 cannot be a prime number.

What is a composite number?

A composite number is a number that has factors other than $$1 and itself. That is, it can be divided evenly by a number some other whole number greater than $$1.

Look at the picture below:

From the dots, we could make $$1 group of $$12, $$2 groups or $$6, $$3 groups of $$4, $$4 groups of $$3, $$6 groups of $$2 or even $$12 groups of $$1.

So the factors of $$12 are $$1,2,3,4,6 and $$12.

Since there are so many ways that these $$12 dots could be split up into equal groups, the number $$12 is an example of a composite number. 

Let's look at some others!

Examples

$$6,14,20 and $$21 are all composite numbers.

$$6 can be written as $$6×1 or $$2×3.

$$14 can be written as $$1×14 or $$2×7.

$$20 can be written as $$20×1 or $$10×2 or $$4×5.

$$21 can be written as $$21×1 or $$3×7.

Can you think of some other composite numbers?

Is it prime or composite?

This question is really asking, can the number be divided by another number other than $$1 or itself? If it can, it is composite. If it can't, it's prime.

Examples

question 1

Is $$17 prime or composite?

$$17 can only be divided by $$1 and $$17, so it is prime.

question 2

Is $$25 a prime number?

$$25 can be divided by $$1 and $$25, but it can also be divided by $$5 so the answer would be no, it is a composite number. 

Practice questions

Question 1

Question 2

Question 3