Greatest Common Factor of 12 and 3

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

• Greatest Common Factor of 12 and 3 by prime factorization method
• Greatest Common Factor of 12 and 3 by matching factors method

Prime Factorization of 12

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

12 = 2²×3¹

Prime Factorization of 3

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

3 = 3¹

∴ So by taking common prime factors GCF of 12 and 3 is 3

Factors of 12

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

1,2,3,4,6,12

Factors of 3

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

1,3

Greatest Common Factor

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

Also check out the Least Common Multiple of 12 and 3

(i) The GCF of 12 and 3 is associative

GCF of 12 and 3 = GCF of 3 and 12

1. What is the GCF of 12 and 3?

Answer: GCF of 12 and 3 is 3.

2. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

3. What are the Factors of 3?

Answer: Factors of 3 are 1, 3. There are 2 integers that are factors of 3. The greatest factor of 3 is 3.

4. How to Find the GCF of 12 and 3?

Answer:

Greatest Common Factor of 12 and 3 = 3

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 2: Find the prime factorization of 3

3 = 3

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 3

Step 4: Therefore, the greatest common factor of 12 and 3 is 3