# What is the Greatest Common Factor of 21 and 38?

Greatest common factor (GCF) of 21 and 38 is 1.

GCF(21,38) = 1

We will now calculate the prime factors of 21 and 38, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21 and 38.

GCF Calculator and
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## How to find the GCF of 21 and 38?

We will first find the prime factorization of 21 and 38. After we will calculate the factors of 21 and 38 and find the biggest common factor number .

### Step-1: Prime Factorization of 21

Prime factors of 21 are 3, 7. Prime factorization of 21 in exponential form is:

21 = 31 × 71

### Step-2: Prime Factorization of 38

Prime factors of 38 are 2, 19. Prime factorization of 38 in exponential form is:

38 = 21 × 191

### Step-3: Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1, 3, 7

### Step-4: Factors of 38

List of positive integer factors of 38 that divides 21 without a remainder.

1, 2, 19

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21 and 38. The biggest common factor number is the GCF number.
So the greatest common factor 21 and 38 is 1.

Also check out the Least Common Multiple of 21 and 38