GCF (HCF) of 54 and 72

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What is the Greatest Common Divisor of 54 and 72?

Answer

GCF (HCF) of 54 and 72 is
18

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

18 divides both: 54 ÷ 18 = 3, 72 ÷ 18 = 4 — and 3 and 4 share no factor but 1, so no larger number divides both.

54 = 2 × 33

72 = 23 × 32

Prime5472Lowest power
22232
3333232

GCF = 2 × 32 = 18

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GCF Table

Number 1Number 2GCF
54573
54582
54591
54606
54611
54622
54639
54642
54651
54666
54671
54682
54693
54702
54711
547218
54731
54742
54753
54762
54771
54786
54791
54802
548127
54822
54831
54846
54851
54862

FAQ

What is the Greatest Common Divisor of 54 and 72?

GCF (HCF) of 54 and 72 is 18

How to find the GCF of 54 and 72?

You can find the GCF of 54 and 72 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 54 and 72 is 18.

What prime factors do 54 and 72 share?

The prime factorizations of 54 and 72 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 54/72?

Divide the numerator and the denominator by the GCF 18: 54 ÷ 18 = 3 and 72 ÷ 18 = 4. So 54/72 in lowest terms is 3/4.

See Also