Factors, multiples and primes | Year 7

01 / LEARN

The idea, step by step

Factors divide exactly

A factor of a whole number divides it with no remainder. Factor pairs help you find a complete list: each pair multiplies to the original number. For 18 the pairs are $1 \times 18$ , $2 \times 9$ and $3 \times 6$ .

A prime number is greater than 1 and has exactly two positive factors: 1 and itself. A composite number has more than two. The number 1 is neither prime nor composite.

Multiples and common values

Multiples are found by multiplying a number by 1, 2, 3 and so on. A common multiple appears in both lists. The lowest common multiple is the smallest positive one.

The highest common factor is the largest number dividing both original numbers exactly. Factors are useful for making equal groups; common multiples are useful for finding when repeating events next happen together.

A common trap

An odd number must be prime.

Instead: Odd composite numbers exist: $21 = 3 \times 7$ . Check factors rather than parity alone.

02 / WORKED EXAMPLES

See the thinking

Example 1

List factors systematically

List every positive factor of 24.

Write factor pairs in increasing order: $1 \times 24$ , $2 \times 12$ , $3 \times 8$ , $4 \times 6$ .
Collect each member of the pairs and order them.

1, 2, 3, 4, 6, 8, 12, 24

Example 2

Find the next shared time

A bell rings every 6 minutes and another every 8 minutes. They ring together now. When will they next ring together?

Positive multiples of 6 begin 6, 12, 18, 24.
Positive multiples of 8 begin 8, 16, 24.
The smallest shared positive time is 24 minutes.

24 minutes

Check your understanding

Is 91 prime?

Show answer

No; it is composite.

$91 = 7 \times 13$ , so it has factors besides 1 and 91.

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

List all positive factors of 36.
3 marks
Write the first four positive multiples of 9.
2 marks
List the prime numbers strictly between 10 and 20.
2 marks
Find the highest common factor of 24 and 40.
2 marks
Find the lowest common multiple of 4 and 6.
2 marks
Thirty students form equal groups. Give every possible group size greater than 1 and less than 30 that leaves nobody out.
3 marks

Read the worked solutions

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

List all positive factors of 36.
3 marks
Use pairs $1 \times 36$ , $2 \times 18$ , $3 \times 12$ , $4 \times 9$ , $6 \times 6$ .
List each factor only once.
1, 2, 3, 4, 6, 9, 12, 18, 36
Write the first four positive multiples of 9.
2 marks
Calculate $9 \times 1$ , $9 \times 2$ , $9 \times 3$ and $9 \times 4$ .
9, 18, 27, 36
List the prime numbers strictly between 10 and 20.
2 marks
Reject 12, 14, 16 and 18 because they are even.
Reject 15 because it is divisible by 3 and 5.
The remaining numbers have no factor besides 1 and themselves.
11, 13, 17, 19
Find the highest common factor of 24 and 40.
2 marks
Common factors are 1, 2, 4 and 8.
The greatest is 8.
8
Find the lowest common multiple of 4 and 6.
2 marks
Multiples of 4 begin 4, 8, 12.
Multiples of 6 begin 6, 12.
The smallest common positive multiple is 12.
12
Thirty students form equal groups. Give every possible group size greater than 1 and less than 30 that leaves nobody out.
3 marks
A possible group size must be a factor of 30.
The factors are 1, 2, 3, 5, 6, 10, 15, 30.
Exclude 1 and 30 as requested.
2, 3, 5, 6, 10, 15

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Place value and powers of ten; efficient whole-number calculations and order of operations; factors, multiples and primes; prime factorisation and exponent notation; square numbers and square roots; estimation and rounding.

Official curriculum source ↗

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