GCF for 6, 12 and 15

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Greatest Common Factor of
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What's the Greatest Common Factor (GCF) of 6, 12 and 15?

Answer

GCF of 6, 12 and 15 is
3

Common factors: 1, 3

3 divides all three: 6 ÷ 3 = 2, 12 ÷ 3 = 4, 15 ÷ 3 = 5 — and 2, 4 and 5 have no factor but 1 common to all of them, so no larger number divides all three.

6 = 2 × 3

12 = 22 × 3

15 = 3 × 5

Prime61215Lowest power
2222——
33333
5——5—

— = power 0: the prime is not a factor of this number, so it cannot be in the GCF.

GCF = 3

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GCF Table

1st2nd3rdGCF
16121
26122
36123
46122
56121
66126
67121
68122
69123
610122
611121
612126
612131
612142
612153
612162
612171
612186
612191
612202
612213
612222
612231
612246
612251
612262
612273
612282
612291
612306

FAQ

What's the Greatest Common Factor (GCF) of 6, 12 and 15?

GCF of 6, 12 and 15 is 3

What prime factors do 6, 12 and 15 share?

All three factorizations contain 3, and multiplying those shared primes gives 3 — exactly the greatest common factor.

Can you get the GCF of 6, 12 and 15 two numbers at a time?

Yes. The GCF of 6 and 12 is 6, and the GCF of 6 and 15 is 3 — the same answer, because the greatest common factor is associative and does not depend on the order of the three numbers.

How does the GCF simplify the ratio 6 : 12 : 15?

Divide every term by the GCF 3: 6 ÷ 3 = 2, 12 ÷ 3 = 4 and 15 ÷ 3 = 5. So 6 : 12 : 15 in lowest terms is 2 : 4 : 5, and no whole number other than 1 divides all three of those.

See Also