GCF for 18, 27 and 30

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

What's the Greatest Common Factor (GCF) of 18, 27 and 30?

Answer

GCF of 18, 27 and 30 is
3

(Three)

3 is the largest positive integer that divides 18, 27 and 30 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 18, 27 and 30 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

All Prime Factors of 27: 3 × 3 × 3 (exponent form: 33)

All Prime Factors of 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

Prime factor182730Lowest power
22—2—
3323333
5——5—

GCF = 3 = 3

Checking the GCF of 18, 27 and 30 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(18, 27) = 9

GCF(9, 30) = 3

GCF(18, 27, 30) = 3

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

18 ÷ 3 = 6

27 ÷ 3 = 9

30 ÷ 3 = 10

6, 9 and 10 have no common factor left — that is what makes 3 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 18, 27 and 30? (The answer is: 3). Enter the first number (e.g. '18'), the second (e.g. '27') and the third (e.g. '30'), 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
1518273
1618271
1718271
1818279
1819271
1820271
1821273
1822271
1823271
1824273
1825271
1826271
1827279
1827281
1827291
1827303
1827311
1827321
1827333
1827341
1827351
1827369
1827371
1827381
1827393
1827401
1827411
1827423
1827431
1827441

FAQ

What's the Greatest Common Factor (GCF) of 18, 27 and 30?

GCF of 18, 27 and 30 is 3

What prime factors do 18, 27 and 30 share?

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

Can you get the GCF of 18, 27 and 30 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 18 and 27 is 9, and the GCF of 9 and 30 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 18 : 27 : 30?

Divide every term by the GCF 3: 18 ÷ 3 = 6, 27 ÷ 3 = 9 and 30 ÷ 3 = 10. So 18 : 27 : 30 in lowest terms is 6 : 9 : 10, and no whole number other than 1 divides all three of those.

See Also