What is the Greatest Common Factor of 6 and 21?

Greatest common factor (GCF) of 6 and 21 is 3.

GCF(6,21) = 3

We will now calculate the prime factors of 6 and 21, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6 and 21.

How to find the GCF of 6 and 21?

We will first find the prime factorization of 6 and 21. After we will calculate the factors of 6 and 21 and find the biggest common factor number .

Step-1: Prime Factorization of 6

Prime factors of 6 are 2, 3. Prime factorization of 6 in exponential form is:

6 = 2¹ × 3¹

Step-2: Prime Factorization of 21

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

21 = 3¹ × 7¹

Step-3: Factors of 6

List of positive integer factors of 6 that divides 6 without a remainder.

1, 2, 3

Step-4: Factors of 21

List of positive integer factors of 21 that divides 6 without a remainder.

1, 3, 7

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6 and 21. The biggest common factor number is the GCF number.
So the greatest common factor 6 and 21 is 3.

Also check out the Least Common Multiple of 6 and 21