GCF for 12, 18 and 21

"Greatest Common Factor of 3 Numbers" Calculator

What's the Greatest Common Factor (GCF) of 12, 18 and 21?

Answer

GCF of 12, 18 and 21 is

Common factors: 1, 3

3 divides all three: 12 ÷ 3 = 4, 18 ÷ 3 = 6, 21 ÷ 3 = 7 — and 4, 6 and 7 have no factor but 1 common to all of them, so no larger number divides all three.

12 = 2² × 3

18 = 2 × 3²

21 = 3 × 7

Prime	12	18	21	Lowest power
2	2²	2	—	—
3	3	3²	3	3
7	—	—	7	—

— = power 0: the prime is not a factor of this number, so it cannot be in the GCF.

GCF = 3

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Related Calculations

GCF Table

1st	2nd	3rd	GCF
6	12	18	6
7	12	18	1
8	12	18	2
9	12	18	3
10	12	18	2
11	12	18	1
12	12	18	6
12	13	18	1
12	14	18	2
12	15	18	3
12	16	18	2
12	17	18	1
12	18	18	6
12	18	19	1
12	18	20	2
12	18	21	3
12	18	22	2
12	18	23	1
12	18	24	6
12	18	25	1
12	18	26	2
12	18	27	3
12	18	28	2
12	18	29	1
12	18	30	6
12	18	31	1
12	18	32	2
12	18	33	3
12	18	34	2
12	18	35	1

FAQ

What's the Greatest Common Factor (GCF) of 12, 18 and 21?

GCF of 12, 18 and 21 is 3

What prime factors do 12, 18 and 21 share?

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

Can you get the GCF of 12, 18 and 21 two numbers at a time?

Yes. The GCF of 12 and 18 is 6, and the GCF of 6 and 21 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 12 : 18 : 21?

Divide every term by the GCF 3: 12 ÷ 3 = 4, 18 ÷ 3 = 6 and 21 ÷ 3 = 7. So 12 : 18 : 21 in lowest terms is 4 : 6 : 7, and no whole number other than 1 divides all three of those.

GCF for 12, 18 and 21

What's the Greatest Common Factor (GCF) of 12, 18 and 21?

More with these numbers

Related Calculations

See Also

GCF Table

FAQ

What's the Greatest Common Factor (GCF) of 12, 18 and 21?

What prime factors do 12, 18 and 21 share?

Can you get the GCF of 12, 18 and 21 two numbers at a time?

How does the GCF simplify the ratio 12 : 18 : 21?

See Also

1st	2nd	3rd	GCF
6	12	18	6
7	12	18	1
8	12	18	2
9	12	18	3
10	12	18	2
11	12	18	1
12	12	18	6
12	13	18	1
12	14	18	2
12	15	18	3
12	16	18	2
12	17	18	1
12	18	18	6
12	18	19	1
12	18	20	2
12	18	21	3
12	18	22	2
12	18	23	1
12	18	24	6
12	18	25	1
12	18	26	2
12	18	27	3
12	18	28	2
12	18	29	1
12	18	30	6
12	18	31	1
12	18	32	2
12	18	33	3
12	18	34	2
12	18	35	1

1st	2nd	3rd	GCF
6	12	18	6
7	12	18	1
8	12	18	2
9	12	18	3
10	12	18	2
11	12	18	1
12	12	18	6
12	13	18	1
12	14	18	2
12	15	18	3
12	16	18	2
12	17	18	1
12	18	18	6
12	18	19	1
12	18	20	2
12	18	21	3
12	18	22	2
12	18	23	1
12	18	24	6
12	18	25	1
12	18	26	2
12	18	27	3
12	18	28	2
12	18	29	1
12	18	30	6
12	18	31	1
12	18	32	2
12	18	33	3
12	18	34	2
12	18	35	1

1st	2nd	3rd	GCF
6	12	18	6
7	12	18	1
8	12	18	2
9	12	18	3
10	12	18	2
11	12	18	1
12	12	18	6
12	13	18	1
12	14	18	2
12	15	18	3
12	16	18	2
12	17	18	1
12	18	18	6
12	18	19	1
12	18	20	2
12	18	21	3
12	18	22	2
12	18	23	1
12	18	24	6
12	18	25	1
12	18	26	2
12	18	27	3
12	18	28	2
12	18	29	1
12	18	30	6
12	18	31	1
12	18	32	2
12	18	33	3
12	18	34	2
12	18	35	1