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HCF of 5 and 9

HCF of 5 and 9 is the largest possible number that divides 5 and 9 exactly without any remainder. The factors of 5 and 9 are 1, 5 and 1, 3, 9 respectively. There are 3 commonly used methods to find the HCF of 5 and 9 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 5 and 9
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 5 and 9?

Answer: HCF of 5 and 9 is 1.

Explanation:

The HCF of two non-zero integers, x(5) and y(9), is the highest positive integer m(1) that divides both x(5) and y(9) without any remainder.

Methods to Find HCF of 5 and 9

The methods to find the HCF of 5 and 9 are explained below.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 5 and 9 by Long Division

HCF of 5 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 5 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (5) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the HCF of 5 and 9.

HCF of 5 and 9 by Listing Common Factors

Factors of 5: 1, 5
Factors of 9: 1, 3, 9

Since, 1 is the only common factor between 5 and 9. The highest common factor of 5 and 9 is 1.

HCF of 5 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 = 5

HCF(9, 5) = HCF(5, 9 mod 5) = HCF(5, 4)
HCF(5, 4) = HCF(4, 5 mod 4) = HCF(4, 1)
HCF(4, 1) = 1 (∵ HCF(X, 1) = 1)

Therefore, the value of HCF of 5 and 9 is 1.

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HCF of 5 and 9 Examples

Example 1: The product of two numbers is 45. If their HCF is 1, what is their LCM?

Solution:

Given: HCF = 1 and product of numbers = 45
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 45/1
Therefore, the LCM is 45.
Example 2: Find the HCF of 5 and 9, if their LCM is 45.

Solution:

∵ LCM × HCF = 5 × 9
⇒ HCF(5, 9) = (5 × 9)/45 = 1
Therefore, the highest common factor of 5 and 9 is 1.
Example 3: For two numbers, HCF = 1 and LCM = 45. If one number is 9, find the other number.

Solution:

Given: HCF (z, 9) = 1 and LCM (z, 9) = 45
∵ HCF × LCM = 9 × (z)
⇒ z = (HCF × LCM)/9
⇒ z = (1 × 45)/9
⇒ z = 5
Therefore, the other number is 5.

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FAQs on HCF of 5 and 9

What is the HCF of 5 and 9?

The HCF of 5 and 9 is 1. To calculate the Highest common factor (HCF) of 5 and 9, we need to factor each number (factors of 5 = 1, 5; factors of 9 = 1, 3, 9) and choose the highest factor that exactly divides both 5 and 9, i.e., 1.

What are the Methods to Find HCF of 5 and 9?

There are three commonly used methods to find the HCF of 5 and 9.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the HCF of 5 and 9 by Long Division Method?

To find the HCF of 5, 9 using long division method, 9 is divided by 5. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 5, 9?

The following equation can be used to express the relation between LCM and HCF of 5 and 9, i.e. HCF × LCM = 5 × 9.

If the HCF of 9 and 5 is 1, Find its LCM.

HCF(9, 5) × LCM(9, 5) = 9 × 5
Since the HCF of 9 and 5 = 1
⇒ 1 × LCM(9, 5) = 45
Therefore, LCM = 45
☛ Highest Common Factor Calculator

How to Find the HCF of 5 and 9 by Prime Factorization?

To find the HCF of 5 and 9, we will find the prime factorization of the given numbers, i.e. 5 = 5; 9 = 3 × 3.
⇒ There is no common prime factor for 5 and 9. Hence, HCF (5, 9) = 1.
☛ What is a Prime Number?

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