GCF for 12, 15 and 21

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
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What's the Greatest Common Factor (GCF) of 12, 15 and 21?

Answer

GCF of 12, 15 and 21 is
3

Common factors: 1, 3

3 divides all three: 12 ÷ 3 = 4, 15 ÷ 3 = 5, 21 ÷ 3 = 7 — and 4, 5 and 7 have no factor but 1 common to all of them, so no larger number divides all three.

12 = 22 × 3

15 = 3 × 5

21 = 3 × 7

Prime121521Lowest power
222———
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
612153
712151
812151
912153
1012151
1112151
1212153
1213151
1214151
1215153
1215161
1215171
1215183
1215191
1215201
1215213
1215221
1215231
1215243
1215251
1215261
1215273
1215281
1215291
1215303
1215311
1215321
1215333
1215341
1215351

FAQ

What's the Greatest Common Factor (GCF) of 12, 15 and 21?

GCF of 12, 15 and 21 is 3

What prime factors do 12, 15 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, 15 and 21 two numbers at a time?

Yes. The GCF of 12 and 15 is 3, and the GCF of 3 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 : 15 : 21?

Divide every term by the GCF 3: 12 ÷ 3 = 4, 15 ÷ 3 = 5 and 21 ÷ 3 = 7. So 12 : 15 : 21 in lowest terms is 4 : 5 : 7, and no whole number other than 1 divides all three of those.

See Also