What is the Greatest Common Factor of 3 and 12?

Greatest common factor (GCF) of 3 and 12 is 3.

GCF(3,12) = 3

We will now calculate the prime factors of 3 and 12, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3 and 12.

How to find the GCF of 3 and 12?

We will first find the prime factorization of 3 and 12. After we will calculate the factors of 3 and 12 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 12

Prime factors of 12 are 2, 3. Prime factorization of 12 in exponential form is:

12 = 2² × 3¹

Step-3: Factors of 3

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

Step-4: Factors of 12

List of positive integer factors of 12 that divides 3 without a remainder.

1, 2, 3, 4, 6

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3 and 12. The biggest common factor number is the GCF number.
So the greatest common factor 3 and 12 is 3.

Also check out the Least Common Multiple of 3 and 12