GCF for 12, 14 and 18

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Greatest Common Factor of
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What's the Greatest Common Factor (GCF) of 12, 14 and 18?

Answer

GCF of 12, 14 and 18 is
2

Common factors: 1, 2

2 divides all three: 12 ÷ 2 = 6, 14 ÷ 2 = 7, 18 ÷ 2 = 9 — and 6, 7 and 9 have no factor but 1 common to all of them, so no larger number divides all three.

12 = 22 × 3

14 = 2 × 7

18 = 2 × 32

Prime121418Lowest power
222222
33—32—
7—7——

— = 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
312141
412142
512141
612142
712141
812142
912141
1012142
1112141
1212142
1213141
1214142
1214151
1214162
1214171
1214182
1214191
1214202
1214211
1214222
1214231
1214242
1214251
1214262
1214271
1214282
1214291
1214302
1214311
1214322

FAQ

What's the Greatest Common Factor (GCF) of 12, 14 and 18?

GCF of 12, 14 and 18 is 2

What prime factors do 12, 14 and 18 share?

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

Can you get the GCF of 12, 14 and 18 two numbers at a time?

Yes. The GCF of 12 and 14 is 2, and the GCF of 2 and 18 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 12 : 14 : 18?

Divide every term by the GCF 2: 12 ÷ 2 = 6, 14 ÷ 2 = 7 and 18 ÷ 2 = 9. So 12 : 14 : 18 in lowest terms is 6 : 7 : 9, and no whole number other than 1 divides all three of those.

See Also