Prime/composite/square numbers | Year 6

01 / LEARN

Understand the idea.

Look for factor pairs

A factor divides a whole number with no remainder. Find factor pairs by starting with $1$ and the number, then trying larger possible factors. Write both members of each pair so that no factor is missed.

A prime number is greater than $1$ and has exactly two positive factors. A composite number is greater than $1$ and has extra factors. Neither $0$ nor $1$ fits these definitions; $2$ is the only even prime.

Recognise squares

A square number makes an array with the same number of rows and columns. The notation $7^{2}$ means $7 \times 7 = 49$ : the small $2$ tells you to use two equal factors, rather than double the number.

The descriptions can overlap. A number such as $36 = 6^{2}$ is square and also composite. When checking factor pairs, stop once the possible smaller factor has passed its equal partner; later pairs would repeat earlier ones.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example 1

Is 29 prime or composite?

Worked solution

1
Start with the certain factor pair.
$29 = 1 \times 29$
Every positive whole number has 1 and itself as factors.
2
Check the remaining possible smaller factors.
$29 \div 2 = 14 remainder 1, 29 \div 3 = 9 remainder 2$
Neither 2 nor 3 divides 29 exactly; 4 cannot divide an odd number and 5 requires a final digit of 0 or 5.
3
Decide when the search is complete.
$5^{2} = 25 < 29 < 36 = 6^{2}$
Any extra factor pair would have a smaller member below 6. All those candidates have been ruled out, so 29 is prime.

Answer

29 is prime.

EXAMPLE 02

Worked example 2

Classify 36 and explain whether it is square.

Worked solution

1
List the factor pairs.
$\begin{array}{c} 36 = 1 \times 36 = 2 \times 18 \\ 36 = 3 \times 12 = 4 \times 9 = 6 \times 6 \end{array}$
Each pair multiplies to 36 and supplies positive factors.
2
Classify using the number of factors.
$1, 2, 3, 4, 6, 9, 12, 18, 36$
There are more than two positive factors, so 36 is composite.
3
Check for equal factors.
$36 = 6 \times 6 = 6^{2}$
Six rows of six form a square array, so 36 is also square.

Answer

36 is composite and square.

03 / YOUR TURN

Try it yourself.

Check your understanding

Is 1 prime? Explain.

Show answer & reasoning

No; it is neither prime nor composite.

$1$ has just one positive factor, itself. A prime needs exactly two, so $1$ is neither prime nor composite.

Keep practising

6 worksheet questions · 10 marks

Open worksheet Worked solutions

Read the questions online

List all positive factors of 18.
2 marks
Classify 17 as prime or composite.
1 mark
Explain why 27 is composite.
2 marks
List the square numbers from 1 to 50.
2 marks
A garden has 8 rows of 8 plants. How many plants?
1 mark
Sam says every square number is composite. Give a counterexample.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

List all positive factors of 18.
2 marks
Use pairs $1 \times 18$ , $2 \times 9$ and $3 \times 6$ .
1, 2, 3, 6, 9, 18.
Classify 17 as prime or composite.
1 mark
Its only positive factors are 1 and 17.
Prime.
Explain why 27 is composite.
2 marks
The pair $3 \times 9$ supplies extra factors.
It has factors 3 and 9 as well as 1 and 27.
List the square numbers from 1 to 50.
2 marks
Calculate $1 \times 1$ through $7 \times 7$ ; $8 \times 8 = 64$ exceeds 50.
1, 4, 9, 16, 25, 36, 49.
A garden has 8 rows of 8 plants. How many plants?
1 mark
$8 \times 8 = 64$ .
64 plants.
Sam says every square number is composite. Give a counterexample.
2 marks
$1 = 1 \times 1$ and has only one positive factor.
1 is square but is not composite.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Prime/composite/square numbers; factors/multiples revision; efficient calculation and estimation.

Official curriculum source ↗

In this lesson

Understand the idea.

Look for factor pairs

Recognise squares

See the method in action.

Worked example 1

Start with the certain factor pair.

Check the remaining possible smaller factors.

Decide when the search is complete.

Worked example 2

List the factor pairs.

Classify using the number of factors.

Check for equal factors.

Try it yourself.

Check your understanding

Keep practising