What is the Greatest Common Factor of 21 and 39?

Greatest common factor (GCF) of 21 and 39 is 3.

GCF(21,39) = 3

We will now calculate the prime factors of 21 and 39, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21 and 39.

How to find the GCF of 21 and 39?

We will first find the prime factorization of 21 and 39. After we will calculate the factors of 21 and 39 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 39

Prime factors of 39 are 3, 13. Prime factorization of 39 in exponential form is:

39 = 3¹ × 13¹

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 39

List of positive integer factors of 39 that divides 21 without a remainder.

1, 3, 13

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21 and 39. The biggest common factor number is the GCF number.
So the greatest common factor 21 and 39 is 3.

Also check out the Least Common Multiple of 21 and 39