# What is the Greatest Common Factor of 72 and 85?

Greatest common factor (GCF) of 72 and 85 is **1**.

GCF(72,85) = 1

We will now calculate the prime factors of **72 and 85**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 72 and 85.

## How to find the GCF of 72 and 85?

We will first find the prime factorization of 72 and 85. After we will calculate the factors of 72 and 85 and find the biggest common factor number .

### Step-1: 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-2: Prime Factorization of 85

Prime factors of 85 are 5, 17. Prime factorization of **85** in exponential form is:

85 = 5^{1} × 17^{1}

### Step-3: Factors of 72

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

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

### Step-4: Factors of 85

List of positive integer factors of 85 that divides 72 without a remainder.

1, 5, 17

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72 and 85. The biggest common factor number is the **GCF** number.

So the **greatest common factor 72 and 85** is **1**.

Also check out the Least Common Multiple of 72 and 85