GCF for 12, 21 and 30

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
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What's the Greatest Common Factor (GCF) of 12, 21 and 30?

Answer

GCF of 12, 21 and 30 is
3

Common factors: 1, 3

3 divides all three: 12 ÷ 3 = 4, 21 ÷ 3 = 7, 30 ÷ 3 = 10 — and 4, 7 and 10 have no factor but 1 common to all of them, so no larger number divides all three.

12 = 22 × 3

21 = 3 × 7

30 = 2 × 3 × 5

Prime122130Lowest power
222—2—
33333
5——5—
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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GCF Table

1st2nd3rdGCF
1215213
1216211
1217211
1218213
1219211
1220211
1221213
1221221
1221231
1221243
1221251
1221261
1221273
1221281
1221291
1221303
1221311
1221321
1221333
1221341
1221351
1221363
1221371
1221381
1221393
1221401
1221411
1221423
1221431
1221441

FAQ

What's the Greatest Common Factor (GCF) of 12, 21 and 30?

GCF of 12, 21 and 30 is 3

What prime factors do 12, 21 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 12, 21 and 30 two numbers at a time?

Yes. The GCF of 12 and 21 is 3, and the GCF of 3 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 12 : 21 : 30?

Divide every term by the GCF 3: 12 ÷ 3 = 4, 21 ÷ 3 = 7 and 30 ÷ 3 = 10. So 12 : 21 : 30 in lowest terms is 4 : 7 : 10, and no whole number other than 1 divides all three of those.

See Also