# What is the Greatest Common Factor of 30 and 45?

Greatest common factor (GCF) of 30 and 45 is **15**.

GCF(30,45) = 15

We will now calculate the prime factors of **30 and 45**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 30 and 45.

## How to find the GCF of 30 and 45?

We will first find the prime factorization of 30 and 45. After we will calculate the factors of 30 and 45 and find the biggest common factor number .

### Step-1: Prime Factorization of 30

Prime factors of 30 are 2, 3, 5. Prime factorization of **30** in exponential form is:

30 = 2^{1} × 3^{1} × 5^{1}

### Step-2: Prime Factorization of 45

Prime factors of 45 are 3, 5. Prime factorization of **45** in exponential form is:

45 = 3^{2} × 5^{1}

### Step-3: Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15

### Step-4: Factors of 45

List of positive integer factors of 45 that divides 30 without a remainder.

1, 3, 5, 9, 15

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30 and 45. The biggest common factor number is the **GCF** number.

So the **greatest common factor 30 and 45** is **15**.

Also check out the Least Common Multiple of 30 and 45

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