What is the Greatest Common Factor of 3 and 21?

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

GCF(3,21) = 3

We will now calculate the prime factors of 3 and 21, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3 and 21.

How to find the GCF of 3 and 21?

We will first find the prime factorization of 3 and 21. After we will calculate the factors of 3 and 21 and find the biggest common factor number .

Step-1: Prime Factorization of 3

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

3 = 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 3

List of positive integer factors of 3 that divides 3 without a remainder.

Step-4: Factors of 21

List of positive integer factors of 21 that divides 3 without a remainder.

1, 3, 7

Final Step: Biggest Common Factor Number

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

Also check out the Least Common Multiple of 3 and 21