GCF for 6, 8 and 12

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Greatest Common Factor of
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What's the Greatest Common Factor (GCF) of 6, 8 and 12?

Answer

GCF of 6, 8 and 12 is
2

Common factors: 1, 2

2 divides all three: 6 ÷ 2 = 3, 8 ÷ 2 = 4, 12 ÷ 2 = 6 — and 3, 4 and 6 have no factor but 1 common to all of them, so no larger number divides all three.

6 = 2 × 3

8 = 23

12 = 22 × 3

Prime6812Lowest power
2223222
33—3—

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

GCF = 2

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GCF Table

1st2nd3rdGCF
1681
2682
3681
4682
5681
6682
6781
6882
6891
68102
68111
68122
68131
68142
68151
68162
68171
68182
68191
68202
68211
68222
68231
68242
68251
68262
68271
68282
68291
68302

FAQ

What's the Greatest Common Factor (GCF) of 6, 8 and 12?

GCF of 6, 8 and 12 is 2

What prime factors do 6, 8 and 12 share?

All three factorizations contain 2, and multiplying those shared primes gives 2 — exactly the greatest common factor.

Can you get the GCF of 6, 8 and 12 two numbers at a time?

Yes. The GCF of 6 and 8 is 2, and the GCF of 2 and 12 is 2 — 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 : 8 : 12?

Divide every term by the GCF 2: 6 ÷ 2 = 3, 8 ÷ 2 = 4 and 12 ÷ 2 = 6. So 6 : 8 : 12 in lowest terms is 3 : 4 : 6, and no whole number other than 1 divides all three of those.

See Also