# What is the Greatest Common Factor of 72 and 90?

Greatest common factor (GCF) of 72 and 90 is **18**.

GCF(72,90) = 18

We will now calculate the prime factors of **72 and 90**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 72 and 90.

## How to find the GCF of 72 and 90?

We will first find the prime factorization of 72 and 90. After we will calculate the factors of 72 and 90 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 90

Prime factors of 90 are 2, 3, 5. Prime factorization of **90** in exponential form is:

90 = 2^{1} × 3^{2} × 5^{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 90

List of positive integer factors of 90 that divides 72 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72 and 90. The biggest common factor number is the **GCF** number.

So the **greatest common factor 72 and 90** is **18**.

Also check out the Least Common Multiple of 72 and 90