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HCF of 9 and 15

HCF of 9 and 15 is the largest possible number that divides 9 and 15 exactly without any remainder. The factors of 9 and 15 are 1, 3, 9 and 1, 3, 5, 15 respectively. There are 3 commonly used methods to find the HCF of 9 and 15 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 9 and 15
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 9 and 15?

Answer: HCF of 9 and 15 is 3.

Explanation:

The HCF of two non-zero integers, x(9) and y(15), is the highest positive integer m(3) that divides both x(9) and y(15) without any remainder.

Methods to Find HCF of 9 and 15

The methods to find the HCF of 9 and 15 are explained below.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

HCF of 9 and 15 by Prime Factorization

Prime factorization of 9 and 15 is (3 × 3) and (3 × 5) respectively. As visible, 9 and 15 have only one common prime factor i.e. 3. Hence, the HCF of 9 and 15 is 3.

HCF of 9 and 15 by Long Division

HCF of 9 and 15 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 15 (larger number) by 9 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (9) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the HCF of 9 and 15.

HCF of 9 and 15 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 = 15 and Y = 9

HCF(15, 9) = HCF(9, 15 mod 9) = HCF(9, 6)
HCF(9, 6) = HCF(6, 9 mod 6) = HCF(6, 3)
HCF(6, 3) = HCF(3, 6 mod 3) = HCF(3, 0)
HCF(3, 0) = 3 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 9 and 15 is 3.

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HCF of 9 and 15 Examples

Example 1: The product of two numbers is 135. If their HCF is 3, what is their LCM?

Solution:

Given: HCF = 3 and product of numbers = 135
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 135/3
Therefore, the LCM is 45.
Example 2: Find the highest number that divides 9 and 15 exactly.

Solution:

The highest number that divides 9 and 15 exactly is their highest common factor, i.e. HCF of 9 and 15.
⇒ Factors of 9 and 15:
- Factors of 9 = 1, 3, 9
- Factors of 15 = 1, 3, 5, 15
Therefore, the HCF of 9 and 15 is 3.
Example 3: Find the HCF of 9 and 15, if their LCM is 45.

Solution:

∵ LCM × HCF = 9 × 15
⇒ HCF(9, 15) = (9 × 15)/45 = 3
Therefore, the highest common factor of 9 and 15 is 3.

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FAQs on HCF of 9 and 15

What is the HCF of 9 and 15?

The HCF of 9 and 15 is 3. To calculate the Highest common factor (HCF) of 9 and 15, we need to factor each number (factors of 9 = 1, 3, 9; factors of 15 = 1, 3, 5, 15) and choose the highest factor that exactly divides both 9 and 15, i.e., 3.

If the HCF of 15 and 9 is 3, Find its LCM.

HCF(15, 9) × LCM(15, 9) = 15 × 9
Since the HCF of 15 and 9 = 3
⇒ 3 × LCM(15, 9) = 135
Therefore, LCM = 45
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How to Find the HCF of 9 and 15 by Prime Factorization?

To find the HCF of 9 and 15, we will find the prime factorization of the given numbers, i.e. 9 = 3 × 3; 15 = 3 × 5.
⇒ Since 3 is the only common prime factor of 9 and 15. Hence, HCF (9, 15) = 3.
☛ What are Prime Numbers?

What are the Methods to Find HCF of 9 and 15?

There are three commonly used methods to find the HCF of 9 and 15.

By Listing Common Factors
By Prime Factorization
By Long Division

What is the Relation Between LCM and HCF of 9, 15?

The following equation can be used to express the relation between Least Common Multiple and HCF of 9 and 15, i.e. HCF × LCM = 9 × 15.

How to Find the HCF of 9 and 15 by Long Division Method?

To find the HCF of 9, 15 using long division method, 15 is divided by 9. The corresponding divisor (3) when remainder equals 0 is taken as HCF.

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