Factors and Multiples
Factors divide a number exactly; multiples are its products with whole numbers.
Key idea
Factors divide a number exactly; multiples are its products with whole numbers.
In depth
A factor divides a number exactly; a multiple is what you get by multiplying it by a whole number. Factors come in pairs and are finite, while multiples go on forever.
Worked example
Factors of 12: 1, 2, 3, 4, 6, 12. Multiples of 12: 12, 24, 36, ...
Real-world uses
- Arranging objects into equal rows
- Finding when two bus routes next meet
- Planning equal groups
Common mistake
Confusing the two words. Factors are small or equal, multiples are large or equal.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Factors and Multiples?
Factors divide a number exactly; multiples are its products with whole numbers. It is a topic at the intermediate level in Arithmetic & Number Sense.
Where is Factors and Multiples used in real life?
Real-world examples: Arranging objects into equal rows; Finding when two bus routes next meet; Planning equal groups.
What should I learn before Factors and Multiples?
Make sure you are comfortable with Long Division, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Factors and Multiples?
Confusing the two words. Factors are small or equal, multiples are large or equal.
How can I practise Factors and Multiples?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Factors and Multiples?
Move on to Divisibility Rules next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.
- Prime Factorization – Every integer above 1 is a unique product of primes.