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HCF of 8 and 15

HCF of 8 and 15 is the largest possible number that divides 8 and 15 exactly without any remainder. The factors of 8 and 15 are 1, 2, 4, 8 and 1, 3, 5, 15 respectively. There are 3 commonly used methods to find the HCF of 8 and 15 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 8 and 15
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 8 and 15?

Answer: HCF of 8 and 15 is 1.

Explanation:

The HCF of two non-zero integers, x(8) and y(15), is the highest positive integer m(1) that divides both x(8) and y(15) without any remainder.

Methods to Find HCF of 8 and 15

Let's look at the different methods for finding the HCF of 8 and 15.

Listing Common Factors
Prime Factorization Method
Long Division Method

HCF of 8 and 15 by Listing Common Factors

Factors of 8: 1, 2, 4, 8
Factors of 15: 1, 3, 5, 15

Since, 1 is the only common factor between 8 and 15. The highest common factor of 8 and 15 is 1.

HCF of 8 and 15 by Prime Factorization

Prime factorization of 8 and 15 is (2 × 2 × 2) and (3 × 5) respectively. As visible, there are no common prime factors between 8 and 15, i.e. they are coprime. Hence, the HCF of 8 and 15 will be 1.

HCF of 8 and 15 by Long Division

HCF of 8 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 8 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (8) by the remainder (7).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the HCF of 8 and 15.

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HCF of 8 and 15 Examples

Example 1: Find the HCF of 8 and 15, if their LCM is 120.

Solution:

∵ LCM × HCF = 8 × 15
⇒ HCF(8, 15) = (8 × 15)/120 = 1
Therefore, the highest common factor of 8 and 15 is 1.
Example 2: Find the highest number that divides 8 and 15 exactly.

Solution:

The highest number that divides 8 and 15 exactly is their highest common factor, i.e. HCF of 8 and 15.
⇒ Factors of 8 and 15:
- Factors of 8 = 1, 2, 4, 8
- Factors of 15 = 1, 3, 5, 15
Therefore, the HCF of 8 and 15 is 1.
Example 3: For two numbers, HCF = 1 and LCM = 120. If one number is 15, find the other number.

Solution:

Given: HCF (y, 15) = 1 and LCM (y, 15) = 120
∵ HCF × LCM = 15 × (y)
⇒ y = (HCF × LCM)/15
⇒ y = (1 × 120)/15
⇒ y = 8
Therefore, the other number is 8.

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FAQs on HCF of 8 and 15

What is the HCF of 8 and 15?

The HCF of 8 and 15 is 1. To calculate the Highest common factor of 8 and 15, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 15 = 1, 3, 5, 15) and choose the highest factor that exactly divides both 8 and 15, i.e., 1.

What are the Methods to Find HCF of 8 and 15?

There are three commonly used methods to find the HCF of 8 and 15.

By Prime Factorization
By Long Division
By Listing Common Factors

If the HCF of 15 and 8 is 1, Find its LCM.

HCF(15, 8) × LCM(15, 8) = 15 × 8
Since the HCF of 15 and 8 = 1
⇒ 1 × LCM(15, 8) = 120
Therefore, LCM = 120
☛ Highest Common Factor Calculator

How to Find the HCF of 8 and 15 by Prime Factorization?

To find the HCF of 8 and 15, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 15 = 3 × 5.
⇒ There is no common prime factor for 8 and 15. Hence, HCF (8, 15) = 1.
☛ What are Prime Numbers?

What is the Relation Between LCM and HCF of 8, 15?

The following equation can be used to express the relation between LCM and HCF of 8 and 15, i.e. HCF × LCM = 8 × 15.

How to Find the HCF of 8 and 15 by Long Division Method?

To find the HCF of 8, 15 using long division method, 15 is divided by 8. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

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