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GCF of 6 and 9

GCF of 6 and 9 is the largest possible number that divides 6 and 9 exactly without any remainder. The factors of 6 and 9 are 1, 2, 3, 6 and 1, 3, 9 respectively. There are 3 commonly used methods to find the GCF of 6 and 9 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 6 and 9
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 6 and 9?

Answer: GCF of 6 and 9 is 3.

Explanation:

The GCF of two non-zero integers, x(6) and y(9), is the greatest positive integer m(3) that divides both x(6) and y(9) without any remainder.

Methods to Find GCF of 6 and 9

Let's look at the different methods for finding the GCF of 6 and 9.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 6 and 9 by Listing Common Factors

Factors of 6: 1, 2, 3, 6
Factors of 9: 1, 3, 9

There are 2 common factors of 6 and 9, that are 1 and 3. Therefore, the greatest common factor of 6 and 9 is 3.

GCF of 6 and 9 by Long Division

GCF of 6 and 9 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 9 (larger number) by 6 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (6) by the remainder (3).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 6 and 9.

GCF of 6 and 9 by Prime Factorization

Prime factorization of 6 and 9 is (2 × 3) and (3 × 3) respectively. As visible, 6 and 9 have only one common prime factor i.e. 3. Hence, the GCF of 6 and 9 is 3.

☛ Also Check:

GCF of 6 and 9 Examples

Example 1: Find the GCF of 6 and 9, if their LCM is 18.

Solution:

∵ LCM × GCF = 6 × 9
⇒ GCF(6, 9) = (6 × 9)/18 = 3
Therefore, the greatest common factor of 6 and 9 is 3.
Example 2: For two numbers, GCF = 3 and LCM = 18. If one number is 9, find the other number.

Solution:

Given: GCF (z, 9) = 3 and LCM (z, 9) = 18
∵ GCF × LCM = 9 × (z)
⇒ z = (GCF × LCM)/9
⇒ z = (3 × 18)/9
⇒ z = 6
Therefore, the other number is 6.
Example 3: Find the greatest number that divides 6 and 9 exactly.

Solution:

The greatest number that divides 6 and 9 exactly is their greatest common factor, i.e. GCF of 6 and 9.
⇒ Factors of 6 and 9:
- Factors of 6 = 1, 2, 3, 6
- Factors of 9 = 1, 3, 9
Therefore, the GCF of 6 and 9 is 3.

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FAQs on GCF of 6 and 9

What is the GCF of 6 and 9?

The GCF of 6 and 9 is 3. To calculate the GCF of 6 and 9, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 9 = 1, 3, 9) and choose the greatest factor that exactly divides both 6 and 9, i.e., 3.

If the GCF of 9 and 6 is 3, Find its LCM.

GCF(9, 6) × LCM(9, 6) = 9 × 6
Since the GCF of 9 and 6 = 3
⇒ 3 × LCM(9, 6) = 54
Therefore, LCM = 18
☛ GCF Calculator

How to Find the GCF of 6 and 9 by Prime Factorization?

To find the GCF of 6 and 9, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 9 = 3 × 3.
⇒ Since 3 is the only common prime factor of 6 and 9. Hence, GCF (6, 9) = 3.
☛ Prime Number

How to Find the GCF of 6 and 9 by Long Division Method?

To find the GCF of 6, 9 using long division method, 9 is divided by 6. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 6 and 9?

There are three commonly used methods to find the GCF of 6 and 9.

By Euclidean Algorithm
By Long Division
By Prime Factorization

What is the Relation Between LCM and GCF of 6, 9?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 6 and 9, i.e. GCF × LCM = 6 × 9.

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