HCF of 9 and 12
HCF 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 HCF of 9 and 12  long division, prime factorization, and Euclidean algorithm.
1.  HCF of 9 and 12 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 9 and 12?
Answer: HCF of 9 and 12 is 3.
Explanation:
The HCF of two nonzero integers, x(9) and y(12), is the highest positive integer m(3) that divides both x(9) and y(12) without any remainder.
Methods to Find HCF of 9 and 12
Let's look at the different methods for finding the HCF of 9 and 12.
 Prime Factorization Method
 Listing Common Factors
 Long Division Method
HCF 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 HCF of 9 and 12 is 3.
HCF 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 highest common factor of 9 and 12 is 3.
HCF of 9 and 12 by Long Division
HCF 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 HCF of 9 and 12.
☛ Also Check:
 HCF of 294, 252 and 210 = 42
 HCF of 650 and 1170 = 130
 HCF of 3 and 6 = 3
 HCF of 2923 and 3239 = 79
 HCF of 72 and 120 = 24
 HCF of 396 and 1080 = 36
 HCF of 28 and 36 = 4
HCF of 9 and 12 Examples

Example 1: For two numbers, HCF = 3 and LCM = 36. If one number is 12, find the other number.
Solution:
Given: HCF (y, 12) = 3 and LCM (y, 12) = 36
∵ HCF × LCM = 12 × (y)
⇒ y = (HCF × LCM)/12
⇒ y = (3 × 36)/12
⇒ y = 9
Therefore, the other number is 9. 
Example 2: The product of two numbers is 108. If their HCF is 3, what is their LCM?
Solution:
Given: HCF = 3 and product of numbers = 108
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 108/3
Therefore, the LCM is 36. 
Example 3: Find the highest number that divides 9 and 12 exactly.
Solution:
The highest number that divides 9 and 12 exactly is their highest common factor, i.e. HCF 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 HCF of 9 and 12 is 3.
FAQs on HCF of 9 and 12
What is the HCF of 9 and 12?
The HCF of 9 and 12 is 3. To calculate the Highest common factor (HCF) 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 highest factor that exactly divides both 9 and 12, i.e., 3.
What is the Relation Between LCM and HCF of 9, 12?
The following equation can be used to express the relation between LCM and HCF of 9 and 12, i.e. HCF × LCM = 9 × 12.
What are the Methods to Find HCF of 9 and 12?
There are three commonly used methods to find the HCF of 9 and 12.
 By Prime Factorization
 By Long Division
 By Euclidean Algorithm
If the HCF of 12 and 9 is 3, Find its LCM.
HCF(12, 9) × LCM(12, 9) = 12 × 9
Since the HCF of 12 and 9 = 3
⇒ 3 × LCM(12, 9) = 108
Therefore, LCM = 36
☛ Highest Common Factor Calculator
How to Find the HCF of 9 and 12 by Long Division Method?
To find the HCF of 9, 12 using long division method, 12 is divided by 9. The corresponding divisor (3) when remainder equals 0 is taken as HCF.
How to Find the HCF of 9 and 12 by Prime Factorization?
To find the HCF 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, HCF (9, 12) = 3.
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