NZ Level 4
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Classify prime or composite (below 100)
Lesson

Prime or composite?

Let's look at some of the rules to help us work out whether a number is prime or composite.

 

Prime numbers

A prime number must be:

  • a whole number
  • a number greater than $1$1
  • only divisible evenly by itself, and $1$1

To be divisible evenly, it means that when we divide by a factor, we don't have any remainder.  In Video 1, we'll look at some numbers to work out if they are prime numbers.

 

Composite numbers

Even though most whole numbers that are not prime numbers are composite numbers, there are some exceptions. First though, let's see what defines a composite number. A composite number must be:

  • a whole number
  • a number greater than $1$1
  • divisible (with no remainders) by other whole numbers, as well as itself and $1$1

In Video 2, we look at how to check if a number is a composite number.

Remember!

$2$2 is the only even number that is NOT a composite number.

 

Neither prime nor composite

Even though $1$1 is divisible only by itself and $1$1, it is not a prime number because it is equal to $1$1, not greater than $1$1. In the same way, the number $0$0 also can't be defined as prime or composite. Remember that one of the rules for both prime and composite numbers is that they must be greater than $1$1.

 

Checking numbers

When we need to determine if a number is a prime or composite number, we can use some things we already know to help us.

Think about the number $70$70. We know that $70\times1=70$70×1=70, but we also know that $7\times10=70$7×10=70, so $70$70 has factors other than $1$1 and itself, which means it must be a composite number. Watch Video 3 to see what other strategies you can use to decide. 

To explore factors in more detail, you may wish to review this topic on divisibility tests.

Remember!
  • $0$0 and $1$1 are neither prime nor composite numbers, as they don't satisfy either definition.
  • Every whole number greater than $1$1 can only be a prime number or a composite number.
  • The number $2$2 is the only even number greater than $1$1 to be a prime number. It's also the only even number greater than $1$1 that is not a composite number.
 

Practice questions

Question 1

Is $2$2 a prime or composite number?

  1. Prime

    A

    Composite

    B

    Prime

    A

    Composite

    B

Question 2

Is $9$9 a prime or composite number?

  1. Prime

    A

    Composite

    B

    Prime

    A

    Composite

    B

Question 3

True or False?

$54$54 is a prime number.

  1. True

    A

    False

    B

    True

    A

    False

    B

Outcomes

NA4-1

Use a range of multiplicative strategies when operating on whole numbers

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