GCF for 36, 60 and 84

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Greatest Common Factor of
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What's the Greatest Common Factor (GCF) of 36, 60 and 84?

Answer

GCF of 36, 60 and 84 is
12

Common factors: 1, 2, 3, 4, 6, 12

12 divides all three: 36 ÷ 12 = 3, 60 ÷ 12 = 5, 84 ÷ 12 = 7 — and 3, 5 and 7 have no factor but 1 common to all of them, so no larger number divides all three.

36 = 22 × 32

60 = 22 × 3 × 5

84 = 22 × 3 × 7

Prime366084Lowest power
222222222
332333
5—5——
7——7—

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

GCF = 22 × 3 = 12

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GCF Table

1st2nd3rdGCF
3660693
3660702
3660711
36607212
3660731
3660742
3660753
3660764
3660771
3660786
3660791
3660804
3660813
3660822
3660831
36608412
3660851
3660862
3660873
3660884
3660891
3660906
3660911
3660924
3660933
3660942
3660951
36609612
3660971
3660982

FAQ

What's the Greatest Common Factor (GCF) of 36, 60 and 84?

GCF of 36, 60 and 84 is 12

What prime factors do 36, 60 and 84 share?

All three factorizations contain 2 × 2 × 3, and multiplying those shared primes gives 12 — exactly the greatest common factor.

Can you get the GCF of 36, 60 and 84 two numbers at a time?

Yes. The GCF of 36 and 60 is 12, and the GCF of 12 and 84 is 12 — 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 36 : 60 : 84?

Divide every term by the GCF 12: 36 ÷ 12 = 3, 60 ÷ 12 = 5 and 84 ÷ 12 = 7. So 36 : 60 : 84 in lowest terms is 3 : 5 : 7, and no whole number other than 1 divides all three of those.

See Also