# What is the Greatest Common Factor of 120 and 126?

Greatest common factor (GCF) of 120 and 126 is 6.

GCF(120,126) = 6

We will now calculate the prime factors of 120 and 126, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 120 and 126.

GCF Calculator and
and

## How to find the GCF of 120 and 126?

We will first find the prime factorization of 120 and 126. After we will calculate the factors of 120 and 126 and find the biggest common factor number .

### Step-1: Prime Factorization of 120

Prime factors of 120 are 2, 3, 5. Prime factorization of 120 in exponential form is:

120 = 23 × 31 × 51

### Step-2: Prime Factorization of 126

Prime factors of 126 are 2, 3, 7. Prime factorization of 126 in exponential form is:

126 = 21 × 32 × 71

### Step-3: Factors of 120

List of positive integer factors of 120 that divides 120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60

### Step-4: Factors of 126

List of positive integer factors of 126 that divides 120 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 120 and 126. The biggest common factor number is the GCF number.
So the greatest common factor 120 and 126 is 6.

Also check out the Least Common Multiple of 120 and 126