# What is the Greatest Common Factor of 54 and 72?

Greatest common factor (GCF) of 54 and 72 is **18**.

GCF(54,72) = 18

We will now calculate the prime factors of **54 and 72**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 54 and 72.

## How to find the GCF of 54 and 72?

We will first find the prime factorization of 54 and 72. After we will calculate the factors of 54 and 72 and find the biggest common factor number .

### Step-1: Prime Factorization of 54

Prime factors of 54 are 2, 3. Prime factorization of **54** in exponential form is:

54 = 2^{1} × 3^{3}

### Step-2: Prime Factorization of 72

Prime factors of 72 are 2, 3. Prime factorization of **72** in exponential form is:

72 = 2^{3} × 3^{2}

### Step-3: Factors of 54

List of positive integer factors of 54 that divides 54 without a remainder.

1, 2, 3, 6, 9, 18, 27

### Step-4: Factors of 72

List of positive integer factors of 72 that divides 54 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54 and 72. The biggest common factor number is the **GCF** number.

So the **greatest common factor 54 and 72** is **18**.

Also check out the Least Common Multiple of 54 and 72

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