Understand the idea.
Factors divide exactly
A positive factor divides a whole number exactly. Find factors in pairs: if , both 2 and 9 are factors. Test smaller partners in order so that a missing pair is easier to spot.
A prime is a whole number greater than 1 with exactly two positive factors, 1 and itself. A composite has additional factors. The number 1 has only one positive factor, so it belongs to neither category.
Multiples and common values
A multiple is produced by multiplying by a whole number. When finding the next shared event, list positive multiples of both intervals. Their smallest common positive value is the lowest common multiple, or LCM.
The highest common factor, or HCF, is instead the largest factor shared by the numbers. Use factors to split quantities into equal groups without leftovers; use multiples to locate shared totals or repeating times.
See the method in action.
List factors systematically
List every positive factor of 24.
Worked solution
- 1
Find the factor pairs.
Each exact product supplies two positive factors.
- 2
Check that the pairs cover every possibility.
Every pair has a smaller partner below 5, and all candidates from 1 to 4 have been checked.
- 3
List each factor once.
Combining both members of every pair gives the complete ordered list.
1, 2, 3, 4, 6, 8, 12, 24
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?
Worked solution
- 1
List the first bell’s times after now.
The first bell rings at positive multiples of 6 minutes.
- 2
List the second bell’s times after now.
The second bell rings at positive multiples of 8 minutes.
- 3
Choose the first shared positive time.
Neither list shares an earlier positive time, so the next simultaneous ring is in 24 minutes.
24 minutes
Try it yourself.
Check your understanding
Is 91 prime?
Show answer & reasoning
No; it is composite.
The factorisation exhibits two factors besides 1 and 91. Therefore 91 is composite, even though it is odd.
Keep practising
6 worksheet questions · 14 marks
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 , , , , .
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 , , and .
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
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 ↗