Factors, Multiples, GCF and LCM
7 min read · Updated September 26, 2026 · by the SolveCalcPro editorial team
Factors and multiples are two sides of multiplication. A factor divides a number exactly; a multiple is what you get by multiplying it. Once you can find them quickly, fractions, ratios and algebra all get easier.
Factors
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36 because each divides 36 with no remainder. Factors come in pairs: 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6.
Multiples
The multiples of 6 are 6, 12, 18, 24, 30 and so on. There are infinitely many multiples but every number has a limited set of factors.
Prime factorization
Every whole number above 1 is a product of primes in exactly one way. 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5. Split the number with a factor tree, or check divisibility with the prime number checker.
Greatest common factor (GCF)
The GCF is the largest factor shared by two or more numbers. For 12 and 18: 12 = 2² × 3 and 18 = 2 × 3², so GCF = 2 × 3 = 6. Use it to simplify fractions and to split things into equal groups: 12 boys and 18 girls can form at most 6 equal teams, each with 2 boys and 3 girls.
Least common multiple (LCM)
The LCM is the smallest number that is a multiple of each. LCM(12, 18) = 2² × 3² = 36. It is the common denominator for adding fractions with those denominators. It also solves timing questions: if one light flashes every 4 seconds and another every 6, they flash together every LCM(4, 6) = 12 seconds.
A handy relationship
For two numbers, GCF × LCM = the product of the numbers. Check: 6 × 36 = 216 = 12 × 18. The GCF and LCM calculator finds both at once.
Practice questions
Test yourself, then tap to check. Answers are calculated by the tools linked below.
- Find the GCF and LCM of 18 and 24.
Show answer
GCF (greatest common factor): 6 · LCM (least common multiple): 72
- Is 221 prime?
Show answer
Is 221 prime?: No, composite
- Add 2/3 + 3/4.
Show answer
Simplified fraction: 17/12
Frequently asked questions
What is the difference between a factor and a multiple?
A factor divides the number; a multiple is the number multiplied by an integer. 3 is a factor of 12 and 12 is a multiple of 3.
Is 1 a factor of every number?
Yes.
What is the GCF of two prime numbers?
1.
When do I use LCM versus GCF?
Use GCF to simplify or split into equal groups; use LCM to find a common denominator or a repeating meeting time.
Try it yourself
GCF and LCM CalculatorFind the greatest common factor and least common multiple of up to 8 numbers.Prime Number CheckerTest whether a number is prime and see its factorization and neighbouring primes.
Fraction CalculatorAdd, subtract, multiply and divide fractions with simplified and mixed-number answers.Keep learning
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