# What is the Greatest Common Factor of 138 and 152?

Greatest common factor (GCF) of 138 and 152 is 2.

GCF(138,152) = 2

We will now calculate the prime factors of 138 and 152, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 138 and 152.

GCF Calculator and
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## How to find the GCF of 138 and 152?

We will first find the prime factorization of 138 and 152. After we will calculate the factors of 138 and 152 and find the biggest common factor number .

### Step-1: Prime Factorization of 138

Prime factors of 138 are 2, 3, 23. Prime factorization of 138 in exponential form is:

138 = 21 × 31 × 231

### Step-2: Prime Factorization of 152

Prime factors of 152 are 2, 19. Prime factorization of 152 in exponential form is:

152 = 23 × 191

### Step-3: Factors of 138

List of positive integer factors of 138 that divides 138 without a remainder.

1, 2, 3, 6, 23, 46, 69

### Step-4: Factors of 152

List of positive integer factors of 152 that divides 138 without a remainder.

1, 2, 4, 8, 19, 38, 76

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 138 and 152. The biggest common factor number is the GCF number.
So the greatest common factor 138 and 152 is 2.

Also check out the Least Common Multiple of 138 and 152