GCF of 54 and 72 (Greatest Common Factor)

"Greatest Common Factor" Calculator
Greatest Common Factor of
and

What is the Greatest Common Divisor of 54 and 72?

Answer

GCF of 54 and 72 is
18

(Eighteen)

Finding GCF for 54 and 72 using all factors (divisors) listing

The first method to find GCF for numbers 54 and 72 is to list all factors for both numbers and pick the highest common one:

All factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

All factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

So the Greatest Common Factor for 54 and 72 is 18

Finding GCF for 54 and 72 by Prime Factorization

The second method to find GCF for numbers 54 and 72 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 54: 2, 3, 3, 3

All Prime Factors of 72: 2, 2, 2, 3, 3

As we can see there are Prime Factors common to both numbers: 2, 3, 3

Now we need to multiply them to find GCF: 2 × 3 × 3 = 18

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About "Greatest Common Factor" Calculator

This calculator will help you find the greatest common factor (GCF) of two numbers. For example, it can help you find out what is the Greatest Common Divisor of 54 and 72? (The answer is: 18). Select the first number (e.g. '54') and the second number (e.g. '72'). After that hit the 'Calculate' button.
Greatest Common Factor (GCF) also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) - it is the largest positive integer that divides each of the integers with zero remainder.
"Greatest Common Factor" Calculator
Greatest Common Factor of
and

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 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