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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 non-zero 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 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.

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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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