Greatest Common Factor of 3 and 6

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

• Greatest Common Factor of 3 and 6 by prime factorization method
• Greatest Common Factor of 3 and 6 by matching factors method

Prime Factorization of 3

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

3 = 3¹

Prime Factorization of 6

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

6 = 2¹×3¹

∴ So by taking common prime factors GCF of 3 and 6 is 3

Factors of 3

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

1,3

Factors of 6

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

1,2,3,6

Greatest Common Factor

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

Also check out the Least Common Multiple of 3 and 6

(i) The GCF of 3 and 6 is associative

GCF of 3 and 6 = GCF of 6 and 3

1. What is the GCF of 3 and 6?

Answer: GCF of 3 and 6 is 3.

2. 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.

3. What are the Factors of 6?

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

4. How to Find the GCF of 3 and 6?

Answer:

Greatest Common Factor of 3 and 6 = 3

Step 1: Find the prime factorization of 3

3 = 3

Step 2: Find the prime factorization of 6

6 = 2 x 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 3 and 6 is 3