GCF (HCF) of 54 and 180

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What is the Greatest Common Divisor of 54 and 180?

Answer

GCF (HCF) of 54 and 180 is
18

Common factors: 1, 2, 3, 6, 9, 18

18 divides both: 54 ÷ 18 = 3, 180 ÷ 18 = 10 — and 3 and 10 share no factor but 1, so no larger number divides both.

54 = 2 × 33

180 = 22 × 32 × 5

Prime54180Lowest power
22222
3333232
5—5—

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

GCF = 2 × 32 = 18

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GCF Table

Number 1Number 2GCF
541653
541662
541671
541686
541691
541702
541719
541722
541731
541746
541751
541762
541773
541782
541791
5418018
541811
541822
541833
541842
541851
541866
541871
541882
5418927
541902
541911
541926
541931
541942

FAQ

What is the Greatest Common Divisor of 54 and 180?

GCF (HCF) of 54 and 180 is 18

How to find the GCF of 54 and 180?

You can find the GCF of 54 and 180 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 54 and 180 is 18.

What prime factors do 54 and 180 share?

The prime factorizations of 54 and 180 have 2 × 3 × 3 in common, and multiplying those shared primes gives 18 — exactly the greatest common factor.

How does the GCF reduce the fraction 54/180?

Divide the numerator and the denominator by the GCF 18: 54 ÷ 18 = 3 and 180 ÷ 18 = 10. So 54/180 in lowest terms is 3/10.

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