Concepts
A factor divides into a number; a multiple is the number multiplied out. 4 is a factor of 12, while 24 is a multiple of 12. They point in opposite directions.
Here's a clear breakdown with a trick you won't forget.
Factors: the numbers that fit inside
A factor divides a number with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12. Factors are always less than or equal to the number. List them with the Factors Calculator.
Multiples: the numbers it builds
A multiple is the number times an integer: 12, 24, 36, 48… Multiples are always greater than or equal to the number and there are infinitely many.
The memory trick
Factors are Few; Multiples are Many. A number has a limited list of factors but an endless list of multiples.
How they connect to GCF and LCM
The GCF is the greatest shared factor; the LCM is the least shared multiple. So factors lead to the GCD and multiples lead to the LCM.
Key takeaways
- Factors divide into a number; multiples are built from it.
- Factors are finite; multiples are infinite.
- 'Factors are Few, Multiples are Many.'
- GCF uses factors; LCM uses multiples.
Frequently asked questions
What is the difference between a factor and a multiple?
A factor divides into the number exactly (4 is a factor of 12); a multiple is the number times an integer (24 is a multiple of 12).
Can a number be both a factor and a multiple of itself?
Yes. Every number is both a factor and a multiple of itself, since n ÷ n = 1 and n × 1 = n.
How many factors and multiples does a number have?
A number has a finite list of factors but infinitely many multiples.
The LCM Calculator Team
Math educators and engineers building free, accurate calculators with step-by-step solutions, visual diagrams and AI insights.
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