HCF of 6 and 9
HCF 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 HCF of 6 and 9  prime factorization, Euclidean algorithm, and long division.
1.  HCF of 6 and 9 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 6 and 9?
Answer: HCF of 6 and 9 is 3.
Explanation:
The HCF of two nonzero integers, x(6) and y(9), is the highest positive integer m(3) that divides both x(6) and y(9) without any remainder.
Methods to Find HCF of 6 and 9
Let's look at the different methods for finding the HCF of 6 and 9.
 Prime Factorization Method
 Listing Common Factors
 Long Division Method
HCF 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 HCF of 6 and 9 is 3.
HCF 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 highest common factor of 6 and 9 is 3.
HCF of 6 and 9 by Long Division
HCF 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 HCF of 6 and 9.
☛ Also Check:
 HCF of 255 and 867 = 51
 HCF of 3, 4 and 5 = 1
 HCF of 1 and 2 = 1
 HCF of 17 and 19 = 1
 HCF of 399 and 437 = 19
 HCF of 60 and 75 = 15
 HCF of 405 and 2520 = 45
HCF of 6 and 9 Examples

Example 1: Find the highest number that divides 6 and 9 exactly.
Solution:
The highest number that divides 6 and 9 exactly is their highest common factor, i.e. HCF of 6 and 9.
⇒ Factors of 6 and 9: Factors of 6 = 1, 2, 3, 6
 Factors of 9 = 1, 3, 9
Therefore, the HCF of 6 and 9 is 3.

Example 2: The product of two numbers is 54. If their HCF is 3, what is their LCM?
Solution:
Given: HCF = 3 and product of numbers = 54
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 54/3
Therefore, the LCM is 18. 
Example 3: For two numbers, HCF = 3 and LCM = 18. If one number is 9, find the other number.
Solution:
Given: HCF (z, 9) = 3 and LCM (z, 9) = 18
∵ HCF × LCM = 9 × (z)
⇒ z = (HCF × LCM)/9
⇒ z = (3 × 18)/9
⇒ z = 6
Therefore, the other number is 6.
FAQs on HCF of 6 and 9
What is the HCF of 6 and 9?
The HCF of 6 and 9 is 3. To calculate the HCF 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 highest factor that exactly divides both 6 and 9, i.e., 3.
What are the Methods to Find HCF of 6 and 9?
There are three commonly used methods to find the HCF of 6 and 9.
 By Euclidean Algorithm
 By Prime Factorization
 By Long Division
How to Find the HCF of 6 and 9 by Long Division Method?
To find the HCF of 6, 9 using long division method, 9 is divided by 6. The corresponding divisor (3) when remainder equals 0 is taken as HCF.
How to Find the HCF of 6 and 9 by Prime Factorization?
To find the HCF 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, HCF (6, 9) = 3.
☛ What are Prime Numbers?
If the HCF of 9 and 6 is 3, Find its LCM.
HCF(9, 6) × LCM(9, 6) = 9 × 6
Since the HCF of 9 and 6 = 3
⇒ 3 × LCM(9, 6) = 54
Therefore, LCM = 18
☛ Highest Common Factor Calculator
What is the Relation Between LCM and HCF of 6, 9?
The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 6 and 9, i.e. HCF × LCM = 6 × 9.
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