Composite Number Definition
Composite numbers are whole numbers that have more than two factors. In other words, a composite number is divisible by the number itself, the number 1, and at least one different number.
The first few composite numbers are 4, 6, 8, 9, and 10.
- For example, the factors of number 4 include 1, 2, and 4. As 4 can be divided by all three of those numbers, it is a composite number.
- 6 has four factors: 1, 2, 3, and 6. (1×6 = 6, 2×3 = 6).
- Factors of 8 are 1, 2, 4, and 8. (1×8 = 8, 2×4 = 8).
- Factors of 9 are 1, 3, and 9. (1×9 = 9 and 3×3 = 9)
What are all the composite numbers up to 100?
Here is a grid with the numbers from 1-100. Highlighted in yellow are all the composite numbers to help children remember them easily. You could print this out and stick it in children’s books or present this page to your child to act as a great visual aid:
Did you know?
- 1 isn’t a composite, but it’s also not a prime number either!
- All even numbers are composite; despite 2, that’s an exception.
- The smallest composite is the number 4!
How do you explain composite numbers to children?
Begin by taking it a step at a time. Usually, children will be introduced to composite numbers at around 7 or 8 years of age during their maths lessons. At this stage, they will just be getting to grips with a simple composite number definition.
You could begin by using visual aids like this table shown above, or provide children with a basic multiplication table like this 100 Number Square, and ask children to highlight all the numbers they think are composite.
Explain that every number higher than one is either a composite or a prime number.
Prime & Composite Numbers
Prime and composite numbers are often grouped in discussions because of their similarities. Here are some quick definitions to get us started:
Prime number definition: A prime number is a whole number with exactly two integral divisors. These are 1 and the number itself.
Many people think 1 is a prime number, but it is not. 1 cannot be a prime number because it only has one divisor.
Composite number definition: A composite number is a whole number with more than 2 integral divisors. Except for 0 and 1, all whole numbers are prime or composite numbers.
Let’s have a look at some examples to put this into practice:
Example 1:
5 is a prime number because its only divisors are 1 and 5.
6 is a composite number because it has multiple divisors. Its divisors are 1, 2, 3, and 6.
How to Tell If a Number is Prime
To tell if a number is prime, you must be able to know if it is not prime. Here are some ways that you can tell if a number is not a prime number:
- As a standard rule, any number more than 2, which is a multiple of 2, is not a prime number. It is because it has at least 3 divisors: 1, 2, and itself. So, because of this rule, we know that 2 is the only even prime number.
- If the number is greater than 3 and is a multiple of 3, it is not a prime number. It is because it has at least three divisors, 1, 3, and itself.
- Any number that is a multiple of 4 is a multiple of 2, so it can be ruled out as not being a prime number.
- Any number greater than 5 and a multiple of 5 is not a prime number. Therefore, the only prime number ending with a 0 or 5 is 5.
- If a number is a multiple of 6, it is also automatically a multiple of both 2 and 3, so it can be immediately ruled out as not a prime number.
To tell if a number is prime, you must look at its divisibility.
Composite or Prime
Let’s have a look at some examples to put our prime and composite number knowledge into practice:
Example 1: Is 17 a prime or composite number?
- The first step is to look at whether it is divisible by 2. Then, without even doing a sum, we know that it is not because 17 is an odd number.
- So, the next step is to see if 17 is divisible by 3. Again, a simple sum will show us that it is not.
- Moreover, because 17 does not end in either 0 or 5, we know that it is not divisible by 5.
- Now we have to see if 17 is divisible by 7. Again, a simple sum will tell us that 17 is not divisible by 7.
- It seems like 17 can’t be divided by numbers except 1 and itself.
- It means that 17 is a prime number.
Example 2: Is 237 a prime or composite number?
- The first step is to check whether 237 is divisible by 2. Without even doing a sum, we can tell that 237 is not divisible by 2 because it is an odd number.
- Next, we must test and see if 237 is divisible by 3. A simple sum will tell us that 237 divided by 3 gives 79.
- It means that 237 is not a prime number because it has multiple divisors.
As it is not a prime number, 237 is a composite number.
Example 3: Is 299 a prime or composite number?
- First, we must check whether or not 299 is divisible by 2. As we have seen before, because 299 is an odd number, we know that it is not divisible by 2.
- So, the next step is to see if 299 is divisible by 3. A simple sum will tell us that 299 is not divisible by 3.
- The following stage requires us to check if 299 is divisible by 5. Because it does not end in a 5 or a 0, we know that 299 is not divisible by 5.
- Now, we have to see if 299 is divisible by 7. A simple sum will tell us that 299 is not divisible by 7.
- It is a trickier example, as 299 is a large number, but you must continue checking whether 299 can be divided by another more significant number. Great opportunity to practice your division skills!
- If you continue to divide 299 by other numbers, you will find that it can be divided by 13 and 23.
It means that 299 is a composite number.Top of Form













