GCF (HCF) of 54 and 90

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What is the Greatest Common Divisor of 54 and 90?

Answer

GCF (HCF) of 54 and 90 is
18

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

18 divides both: 54 ÷ 18 = 3, 90 ÷ 18 = 5 — and 3 and 5 share no factor but 1, so no larger number divides both.

54 = 2 × 33

90 = 2 × 32 × 5

Prime5490Lowest power
2222
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
54753
54762
54771
54786
54791
54802
548127
54822
54831
54846
54851
54862
54873
54882
54891
549018
54911
54922
54933
54942
54951
54966
54971
54982
54999
541002
541011
541026
541031
541042

FAQ

What is the Greatest Common Divisor of 54 and 90?

GCF (HCF) of 54 and 90 is 18

How to find the GCF of 54 and 90?

You can find the GCF of 54 and 90 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 54 and 90 is 18.

What prime factors do 54 and 90 share?

The prime factorizations of 54 and 90 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 54/90?

Divide the numerator and the denominator by the GCF 18: 54 ÷ 18 = 3 and 90 ÷ 18 = 5. So 54/90 in lowest terms is 3/5.

See Also