GCF for 12, 18 and 20

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
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What's the Greatest Common Factor (GCF) of 12, 18 and 20?

Answer

GCF of 12, 18 and 20 is
2

(Two)

2 is the largest positive integer that divides 12, 18 and 20 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 12, 18 and 20 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)

Prime factor121820Lowest power
2222222
3332——
5——5—

GCF = 2 = 2

Checking the GCF of 12, 18 and 20 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, 18) = 6

GCF(6, 20) = 2

GCF(12, 18, 20) = 2

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

12 ÷ 2 = 6

18 ÷ 2 = 9

20 ÷ 2 = 10

6, 9 and 10 have no common factor left — that is what makes 2 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 12, 18 and 20? (The answer is: 2). Enter the first number (e.g. '12'), the second (e.g. '18') and the third (e.g. '20'), 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
512181
612186
712181
812182
912183
1012182
1112181
1212186
1213181
1214182
1215183
1216182
1217181
1218186
1218191
1218202
1218213
1218222
1218231
1218246
1218251
1218262
1218273
1218282
1218291
1218306
1218311
1218322
1218333
1218342

FAQ

What's the Greatest Common Factor (GCF) of 12, 18 and 20?

GCF of 12, 18 and 20 is 2

What prime factors do 12, 18 and 20 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, 18 and 20 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 12 and 18 is 6, and the GCF of 6 and 20 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 : 18 : 20?

Divide every term by the GCF 2: 12 ÷ 2 = 6, 18 ÷ 2 = 9 and 20 ÷ 2 = 10. So 12 : 18 : 20 in lowest terms is 6 : 9 : 10, and no whole number other than 1 divides all three of those.

See Also