GCF for 12, 14 and 18

"Greatest Common Factor of 3 Numbers" Calculator
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

(Two)

2 is the largest positive integer that divides 12, 14 and 18 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 12, 14 and 18 by Prime Factorization

Split all three numbers into prime factors, then keep every prime that appears in all three of them, each taken as many times as it appears in the poorest factorization. Multiplying what is left gives the greatest common factor:

All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

All Prime Factors of 14: 2 × 7 (exponent form: 2 × 7)

All Prime Factors of 18: 2 × 3 × 3 (exponent form: 2 × 32)

Prime factor121418Lowest power
222222
33—32—
7—7——

GCF = 2 = 2

Checking the GCF of 12, 14 and 18 Two Numbers at a Time

The greatest common factor is associative, so three numbers can be handled as two pairs — and this is what makes the Euclidean algorithm usable here: run it on the first pair, then run it again on that result and the third number.

GCF(a, b, c) = GCF(GCF(a, b), c)

GCF(12, 14) = 2

GCF(2, 18) = 2

GCF(12, 14, 18) = 2

The answer checks out by division — all three quotients come out whole:

12 ÷ 2 = 6

14 ÷ 2 = 7

18 ÷ 2 = 9

6, 7 and 9 have no common factor left — that is what makes 2 the greatest one.

Related Calculations

See Also

About "Greatest Common Factor of 3 Numbers" Calculator

This calculator finds the Greatest Common Factor (GCF) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Greatest Common Factor (GCF) of 12, 14 and 18? (The answer is: 2). Enter the first number (e.g. '12'), the second (e.g. '14') and the third (e.g. '18'), then hit the 'Calculate' button.
The Greatest Common Factor of three numbers — also called the greatest common divisor (GCD) or highest common factor (HCF) — is the largest positive integer that divides all three of them with zero remainder
"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
and

GCF Table

Number 1Number 2Number 3GCF
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, and it is the check this page prints. 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