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GCF (HCF) of 54 and 72

"Greatest Common Factor" Calculator

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

Prime	54	72	Lowest power
2	2	2³	2
3	3³	3²	3²

GCF = 2 × 3² = 18

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See Also

Least Common Multiple - Find the Least Common Multiple (LCM) of two numbers
Greatest Common Factor of 3 Numbers - Find the Greatest Common Factor (GCF) of three numbers
Least Common Multiple of 3 Numbers - Find the Least Common Multiple (LCM) of three numbers

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What is the GCF (HCF) of 54 and 72. The GCF of 54 and 72 is 18 — the biggest number that can divide both integers. Step-by-step GCF (GCD) calculation by factoring.

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GCF Table

Number 1	Number 2	GCF
54	57	3
54	58	2
54	59	1
54	60	6
54	61	1
54	62	2
54	63	9
54	64	2
54	65	1
54	66	6
54	67	1
54	68	2
54	69	3
54	70	2
54	71	1
54	72	18
54	73	1
54	74	2
54	75	3
54	76	2
54	77	1
54	78	6
54	79	1
54	80	2
54	81	27
54	82	2
54	83	1
54	84	6
54	85	1
54	86	2

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.