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GCF of 9 and 12

GCF of 9 and 12 is the largest possible number that divides 9 and 12 exactly without any remainder. The factors of 9 and 12 are 1, 3, 9 and 1, 2, 3, 4, 6, 12 respectively. There are 3 commonly used methods to find the GCF of 9 and 12 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 9 and 12
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 9 and 12?

Answer: GCF of 9 and 12 is 3.

Explanation:

The GCF of two non-zero integers, x(9) and y(12), is the greatest positive integer m(3) that divides both x(9) and y(12) without any remainder.

Methods to Find GCF of 9 and 12

The methods to find the GCF of 9 and 12 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 9 and 12 by Long Division

GCF of 9 and 12 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 12 (larger number) by 9 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (9) by the remainder (3).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 9 and 12.

GCF of 9 and 12 by Prime Factorization

Prime factorization of 9 and 12 is (3 × 3) and (2 × 2 × 3) respectively. As visible, 9 and 12 have only one common prime factor i.e. 3. Hence, the GCF of 9 and 12 is 3.

GCF of 9 and 12 by Listing Common Factors

Factors of 9: 1, 3, 9
Factors of 12: 1, 2, 3, 4, 6, 12

There are 2 common factors of 9 and 12, that are 1 and 3. Therefore, the greatest common factor of 9 and 12 is 3.

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GCF of 9 and 12 Examples

Example 1: The product of two numbers is 108. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 108
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 108/3
Therefore, the LCM is 36.
Example 2: Find the GCF of 9 and 12, if their LCM is 36.

Solution:

∵ LCM × GCF = 9 × 12
⇒ GCF(9, 12) = (9 × 12)/36 = 3
Therefore, the greatest common factor of 9 and 12 is 3.
Example 3: Find the greatest number that divides 9 and 12 exactly.

Solution:

The greatest number that divides 9 and 12 exactly is their greatest common factor, i.e. GCF of 9 and 12.
⇒ Factors of 9 and 12:
- Factors of 9 = 1, 3, 9
- Factors of 12 = 1, 2, 3, 4, 6, 12
Therefore, the GCF of 9 and 12 is 3.

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FAQs on GCF of 9 and 12

What is the GCF of 9 and 12?

The GCF of 9 and 12 is 3. To calculate the GCF (Greatest Common Factor) of 9 and 12, we need to factor each number (factors of 9 = 1, 3, 9; factors of 12 = 1, 2, 3, 4, 6, 12) and choose the greatest factor that exactly divides both 9 and 12, i.e., 3.

How to Find the GCF of 9 and 12 by Prime Factorization?

To find the GCF of 9 and 12, we will find the prime factorization of the given numbers, i.e. 9 = 3 × 3; 12 = 2 × 2 × 3.
⇒ Since 3 is the only common prime factor of 9 and 12. Hence, GCF (9, 12) = 3.
☛ Prime Number

What is the Relation Between LCM and GCF of 9, 12?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 9 and 12, i.e. GCF × LCM = 9 × 12.

How to Find the GCF of 9 and 12 by Long Division Method?

To find the GCF of 9, 12 using long division method, 12 is divided by 9. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

If the GCF of 12 and 9 is 3, Find its LCM.

GCF(12, 9) × LCM(12, 9) = 12 × 9
Since the GCF of 12 and 9 = 3
⇒ 3 × LCM(12, 9) = 108
Therefore, LCM = 36
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 9 and 12?

There are three commonly used methods to find the GCF of 9 and 12.

By Prime Factorization
By Long Division
By Euclidean Algorithm

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