GCF for 12, 16 and 18

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
and

What's the Greatest Common Factor (GCF) of 12, 16 and 18?

Answer

GCF of 12, 16 and 18 is
2

(Two)

2 is the largest positive integer that divides 12, 16 and 18 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 12, 16 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

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

Prime factor121618Lowest power
2222422
33—32—

GCF = 2 = 2

Checking the GCF of 12, 16 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, 16) = 4

GCF(4, 18) = 2

GCF(12, 16, 18) = 2

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

12 ÷ 2 = 6

16 ÷ 2 = 8

18 ÷ 2 = 9

6, 8 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, 16 and 18? (The answer is: 2). Enter the first number (e.g. '12'), the second (e.g. '16') 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
312161
412164
512161
612162
712161
812164
912161
1012162
1112161
1212164
1213161
1214162
1215161
1216164
1216171
1216182
1216191
1216204
1216211
1216222
1216231
1216244
1216251
1216262
1216271
1216284
1216291
1216302
1216311
1216324

FAQ

What's the Greatest Common Factor (GCF) of 12, 16 and 18?

GCF of 12, 16 and 18 is 2

What prime factors do 12, 16 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, 16 and 18 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 12 and 16 is 4, and the GCF of 4 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 : 16 : 18?

Divide every term by the GCF 2: 12 ÷ 2 = 6, 16 ÷ 2 = 8 and 18 ÷ 2 = 9. So 12 : 16 : 18 in lowest terms is 6 : 8 : 9, and no whole number other than 1 divides all three of those.

See Also