# What is the Greatest Common Factor of 114 and 133?

Greatest common factor (GCF) of 114 and 133 is 19.

GCF(114,133) = 19

We will now calculate the prime factors of 114 and 133, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 114 and 133.

GCF Calculator and
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## How to find the GCF of 114 and 133?

We will first find the prime factorization of 114 and 133. After we will calculate the factors of 114 and 133 and find the biggest common factor number .

### Step-1: Prime Factorization of 114

Prime factors of 114 are 2, 3, 19. Prime factorization of 114 in exponential form is:

114 = 21 × 31 × 191

### Step-2: Prime Factorization of 133

Prime factors of 133 are 7, 19. Prime factorization of 133 in exponential form is:

133 = 71 × 191

### Step-3: Factors of 114

List of positive integer factors of 114 that divides 114 without a remainder.

1, 2, 3, 6, 19, 38, 57

### Step-4: Factors of 133

List of positive integer factors of 133 that divides 114 without a remainder.

1, 7, 19

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 114 and 133. The biggest common factor number is the GCF number.
So the greatest common factor 114 and 133 is 19.

Also check out the Least Common Multiple of 114 and 133