Greatest Common Factor of 6 and 9

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

• Greatest Common Factor of 6 and 9 by prime factorization method
• Greatest Common Factor of 6 and 9 by matching factors method

Prime Factorization of 6

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

6 = 2¹×3¹

Prime Factorization of 9

Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:

9 = 3²

∴ So by taking common prime factors GCF of 6 and 9 is 3

Factors of 6

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

1,2,3,6

Factors of 9

List of positive integer factors of 9 that divides 9 without a remainder.

1,3,9

Greatest Common Factor

We found the factors and prime factorization of 6 and 9. The biggest common factor number is the GCF number.
So the greatest common factor 6 and 9 is 3.

Also check out the Least Common Multiple of 6 and 9

(i) The GCF of 6 and 9 is associative

GCF of 6 and 9 = GCF of 9 and 6

1. What is the GCF of 6 and 9?

Answer: GCF of 6 and 9 is 3.

2. 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.

3. What are the Factors of 9?

Answer: Factors of 9 are 1, 3, 9. There are 3 integers that are factors of 9. The greatest factor of 9 is 9.

4. How to Find the GCF of 6 and 9?

Answer:

Greatest Common Factor of 6 and 9 = 3

Step 1: Find the prime factorization of 6

6 = 2 x 3

Step 2: Find the prime factorization of 9

9 = 3 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 6 and 9 is 3