GCF of 6 and 9
The greatest common factor of 6 and 9 is 3. Their least common multiple is 18.
- Answer with working
- LCM included
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Why the GCF of 6 and 9 is 3
- Break each number into primes: 6 = 2 × 3 and 9 = 3².
- Keep only the primes in both lists, each at its lower power: 3.
- Multiply those together: the GCF is 3.
The factors 6 and 9 share are 1, 3. The largest of them is 3, which is another way of getting the same answer.
For the least common multiple, take every prime at its higher power instead: the LCM of 6 and 9 is 18. A quick check: 6 × 9 = 54, and 54 ÷ 3 = 18.
Find the GCF
Whole numbers, separated by spaces, commas or new lines.
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How to find the greatest common factor
Factor each number
24 = 2³ × 3, 36 = 2² × 3², 60 = 2² × 3 × 5.
Keep the shared primes
Take each prime that appears in every number, at its lowest power: 2² and 3.
Multiply them
2² × 3 = 12. The GCF of 24, 36 and 60 is 12. For the LCM, take every prime at its highest power: 2³ × 3² × 5 = 360.
GCF is also called GCD (greatest common divisor) and HCF (highest common factor). Same thing.
Questions people ask
What is the GCF of 6 and 9?
3. It is the largest whole number that divides both 6 and 9 exactly.
What is the LCM of 6 and 9?
18. It is the smallest whole number that both 6 and 9 divide into.
What are the common factors of 6 and 9?
1, 3. The greatest of them, 3, is the GCF.
Is GCF the same as GCD and HCF?
Yes. Greatest common factor, greatest common divisor and highest common factor all mean the same thing.
What is the difference between GCF and LCM?
GCF is the biggest number that divides into all of them; LCM is the smallest number they all divide into. For 4 and 6, the GCF is 2 and the LCM is 12.
What is the GCF if one number is 0?
The GCF of 0 and any number n is n itself, because every number divides 0. The LCM with 0 is undefined.
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