# What is the Greatest Common Factor of 90 and 108?

Greatest common factor (GCF) of 90 and 108 is **18**.

GCF(90,108) = 18

We will now calculate the prime factors of **90 and 108**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 90 and 108.

## How to find the GCF of 90 and 108?

We will first find the prime factorization of 90 and 108. After we will calculate the factors of 90 and 108 and find the biggest common factor number .

### Step-1: 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-2: Prime Factorization of 108

Prime factors of 108 are 2, 3. Prime factorization of **108** in exponential form is:

108 = 2^{2} × 3^{3}

### Step-3: Factors of 90

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

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

### Step-4: Factors of 108

List of positive integer factors of 108 that divides 90 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 90 and 108. The biggest common factor number is the **GCF** number.

So the **greatest common factor 90 and 108** is **18**.

Also check out the Least Common Multiple of 90 and 108

#### Related Greatest Common Factors of 90

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