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 nonzero 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.
☛ Also Check:
 GCF of 92 and 23 = 23
 GCF of 34 and 85 = 17
 GCF of 15 and 64 = 1
 GCF of 28 and 72 = 4
 GCF of 32 and 36 = 4
 GCF of 36 and 90 = 18
 GCF of 20 and 28 = 4
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.
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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