GCF (HCF) of 84 and 60

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What is the Greatest Common Divisor of 84 and 60?

Answer

GCF (HCF) of 84 and 60 is
12

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

12 divides both: 84 ÷ 12 = 7, 60 ÷ 12 = 5 — and 7 and 5 share no factor but 1, so no larger number divides both.

84 = 22 × 3 × 7

60 = 22 × 3 × 5

Prime8460Lowest power
2222222
3333
5—5—
77——

— = 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

Number 1Number 2GCF
84453
84462
84471
844812
84497
84502
84513
84524
84531
84546
84551
845628
84573
84582
84591
846012
84611
84622
846321
84644
84651
84666
84671
84684
84693
847014
84711
847212
84731
84742

FAQ

What is the Greatest Common Divisor of 84 and 60?

GCF (HCF) of 84 and 60 is 12

How to find the GCF of 84 and 60?

You can find the GCF of 84 and 60 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 84 and 60 is 12.

What prime factors do 84 and 60 share?

The prime factorizations of 84 and 60 have 2 × 2 × 3 in common, and multiplying those shared primes gives 12 — exactly the greatest common factor.

How does the GCF reduce the fraction 84/60?

Divide the numerator and the denominator by the GCF 12: 84 ÷ 12 = 7 and 60 ÷ 12 = 5. So 84/60 in lowest terms is 7/5.

See Also