GCF for 8, 12 and 16

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
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What's the Greatest Common Factor (GCF) of 8, 12 and 16?

Answer

GCF of 8, 12 and 16 is
4

Common factors: 1, 2, 4

4 divides all three: 8 ÷ 4 = 2, 12 ÷ 4 = 3, 16 ÷ 4 = 4 — and 2, 3 and 4 have no factor but 1 common to all of them, so no larger number divides all three.

8 = 23

12 = 22 × 3

16 = 24

Prime81216Lowest power
223222422
3—3——

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

GCF = 22 = 4

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GCF Table

1st2nd3rdGCF
18121
28122
38121
48124
58121
68122
78121
88124
89121
810122
811121
812124
812131
812142
812151
812164
812171
812182
812191
812204
812211
812222
812231
812244
812251
812262
812271
812284
812291
812302

FAQ

What's the Greatest Common Factor (GCF) of 8, 12 and 16?

GCF of 8, 12 and 16 is 4

What prime factors do 8, 12 and 16 share?

All three factorizations contain 2 × 2, and multiplying those shared primes gives 4 — exactly the greatest common factor.

Can you get the GCF of 8, 12 and 16 two numbers at a time?

Yes. The GCF of 8 and 12 is 4, and the GCF of 4 and 16 is 4 — 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 8 : 12 : 16?

Divide every term by the GCF 4: 8 ÷ 4 = 2, 12 ÷ 4 = 3 and 16 ÷ 4 = 4. So 8 : 12 : 16 in lowest terms is 2 : 3 : 4, and no whole number other than 1 divides all three of those.

See Also