GCF for 9, 12 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 9, 12 and 18?

Answer

GCF of 9, 12 and 18 is
3

(Three)

3 is the largest positive integer that divides 9, 12 and 18 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 9, 12 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 9: 3 × 3 (exponent form: 32)

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

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

Prime factor91218Lowest power
2—222—
3323323

GCF = 3 = 3

Checking the GCF of 9, 12 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(9, 12) = 3

GCF(3, 18) = 3

GCF(9, 12, 18) = 3

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

9 ÷ 3 = 3

12 ÷ 3 = 4

18 ÷ 3 = 6

3, 4 and 6 have no common factor left — that is what makes 3 the greatest one.

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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 9, 12 and 18? (The answer is: 3). Enter the first number (e.g. '9'), the second (e.g. '12') 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
39123
49121
59121
69123
79121
89121
99123
910121
911121
912123
912131
912141
912153
912161
912171
912183
912191
912201
912213
912221
912231
912243
912251
912261
912273
912281
912291
912303
912311
912321

FAQ

What's the Greatest Common Factor (GCF) of 9, 12 and 18?

GCF of 9, 12 and 18 is 3

What prime factors do 9, 12 and 18 share?

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

Can you get the GCF of 9, 12 and 18 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 9 and 12 is 3, and the GCF of 3 and 18 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 9 : 12 : 18?

Divide every term by the GCF 3: 9 ÷ 3 = 3, 12 ÷ 3 = 4 and 18 ÷ 3 = 6. So 9 : 12 : 18 in lowest terms is 3 : 4 : 6, and no whole number other than 1 divides all three of those.

See Also