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HCF of 7 and 9

HCF of 7 and 9 is the largest possible number that divides 7 and 9 exactly without any remainder. The factors of 7 and 9 are 1, 7 and 1, 3, 9 respectively. There are 3 commonly used methods to find the HCF of 7 and 9 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 7 and 9
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 7 and 9?

Answer: HCF of 7 and 9 is 1.

Explanation:

The HCF of two non-zero integers, x(7) and y(9), is the highest positive integer m(1) that divides both x(7) and y(9) without any remainder.

Methods to Find HCF of 7 and 9

Let's look at the different methods for finding the HCF of 7 and 9.

Prime Factorization Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 7 and 9 by Prime Factorization

Prime factorization of 7 and 9 is (7) and (3 × 3) respectively. As visible, there are no common prime factors between 7 and 9, i.e. they are coprime. Hence, the HCF of 7 and 9 will be 1.

HCF of 7 and 9 by Listing Common Factors

Factors of 7: 1, 7
Factors of 9: 1, 3, 9

Since, 1 is the only common factor between 7 and 9. The highest common factor of 7 and 9 is 1.

HCF of 7 and 9 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 9 and Y = 7

HCF(9, 7) = HCF(7, 9 mod 7) = HCF(7, 2)
HCF(7, 2) = HCF(2, 7 mod 2) = HCF(2, 1)
HCF(2, 1) = 1 (∵ HCF(X, 1) = 1)

Therefore, the value of HCF of 7 and 9 is 1.

☛ Also Check:

HCF of 7 and 9 Examples

Example 1: Find the highest number that divides 7 and 9 exactly.

Solution:

The highest number that divides 7 and 9 exactly is their highest common factor, i.e. HCF of 7 and 9.
⇒ Factors of 7 and 9:
- Factors of 7 = 1, 7
- Factors of 9 = 1, 3, 9
Therefore, the HCF of 7 and 9 is 1.
Example 2: For two numbers, HCF = 1 and LCM = 63. If one number is 9, find the other number.

Solution:

Given: HCF (x, 9) = 1 and LCM (x, 9) = 63
∵ HCF × LCM = 9 × (x)
⇒ x = (HCF × LCM)/9
⇒ x = (1 × 63)/9
⇒ x = 7
Therefore, the other number is 7.
Example 3: The product of two numbers is 63. If their HCF is 1, what is their LCM?

Solution:

Given: HCF = 1 and product of numbers = 63
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 63/1
Therefore, the LCM is 63.

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FAQs on HCF of 7 and 9

What is the HCF of 7 and 9?

The HCF of 7 and 9 is 1. To calculate the Highest common factor (HCF) of 7 and 9, we need to factor each number (factors of 7 = 1, 7; factors of 9 = 1, 3, 9) and choose the highest factor that exactly divides both 7 and 9, i.e., 1.

If the HCF of 9 and 7 is 1, Find its LCM.

HCF(9, 7) × LCM(9, 7) = 9 × 7
Since the HCF of 9 and 7 = 1
⇒ 1 × LCM(9, 7) = 63
Therefore, LCM = 63
☛ HCF Calculator

How to Find the HCF of 7 and 9 by Prime Factorization?

To find the HCF of 7 and 9, we will find the prime factorization of the given numbers, i.e. 7 = 7; 9 = 3 × 3.
⇒ There is no common prime factor for 7 and 9. Hence, HCF (7, 9) = 1.
☛ Prime Numbers

How to Find the HCF of 7 and 9 by Long Division Method?

To find the HCF of 7, 9 using long division method, 9 is divided by 7. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 7, 9?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 7 and 9, i.e. HCF × LCM = 7 × 9.

What are the Methods to Find HCF of 7 and 9?

There are three commonly used methods to find the HCF of 7 and 9.

By Long Division
By Prime Factorization
By Listing Common Factors

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