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HCF of 7 and 8

HCF of 7 and 8 is the largest possible number that divides 7 and 8 exactly without any remainder. The factors of 7 and 8 are 1, 7 and 1, 2, 4, 8 respectively. There are 3 commonly used methods to find the HCF of 7 and 8 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 7 and 8
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 7 and 8?

Answer: HCF of 7 and 8 is 1.

Explanation:

The HCF of two non-zero integers, x(7) and y(8), is the highest positive integer m(1) that divides both x(7) and y(8) without any remainder.

Methods to Find HCF of 7 and 8

Let's look at the different methods for finding the HCF of 7 and 8.

Listing Common Factors
Prime Factorization Method
Long Division Method

HCF of 7 and 8 by Listing Common Factors

Factors of 7: 1, 7
Factors of 8: 1, 2, 4, 8

Since 1 is the only common factor between 7 and 8. The highest common factor of 7 and 8 is 1.

HCF of 7 and 8 by Prime Factorization

Prime factorization of 7 and 8 is (7) and (2 × 2 × 2) respectively. As visible, there are no common prime factors between 7 and 8, i.e. they are co-prime. Hence, the HCF of 7 and 8 will be 1.

HCF of 7 and 8 by Long Division

HCF of 7 and 8 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

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

The corresponding divisor (1) is the HCF of 7 and 8.

☛ Also Check:

HCF of 7 and 8 Examples

Example 1: Find the HCF of 7 and 8, if their LCM is 56.

Solution:

∵ LCM × HCF = 7 × 8
⇒ HCF(7, 8) = (7 × 8)/56 = 1
Therefore, the highest common factor of 7 and 8 is 1.
Example 2: The product of two numbers is 56. If their HCF is 1, what is their LCM?

Solution:

Given: HCF = 1 and product of numbers = 56
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 56/1
Therefore, the LCM is 56.
Example 3: Find the highest number that divides 7 and 8 exactly.

Solution:

The highest number that divides 7 and 8 exactly is their highest common factor, i.e. HCF of 7 and 8.
⇒ Factors of 7 and 8:
- Factors of 7 = 1, 7
- Factors of 8 = 1, 2, 4, 8
Therefore, the HCF of 7 and 8 is 1.

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FAQs on HCF of 7 and 8

What is the HCF of 7 and 8?

The HCF of 7 and 8 is 1. To calculate the Highest common factor of 7 and 8, we need to factor each number (factors of 7 = 1, 7; factors of 8 = 1, 2, 4, 8) and choose the highest factor that exactly divides both 7 and 8, i.e., 1.

What are the Methods to Find HCF of 7 and 8?

There are three commonly used methods to find the HCF of 7 and 8.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the HCF of 7 and 8 by Prime Factorization?

To find the HCF of 7 and 8, we will find the prime factorization of the given numbers, i.e. 7 = 7; 8 = 2 × 2 × 2.
⇒ There is no common prime factor for 7 and 8. Hence, HCF (7, 8) = 1.
☛ Prime Number

What is the Relation Between LCM and HCF of 7, 8?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 7 and 8, i.e. HCF × LCM = 7 × 8.

How to Find the HCF of 7 and 8 by Long Division Method?

To find the HCF of 7, 8 using long division method, 8 is divided by 7. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

If the HCF of 8 and 7 is 1, Find its LCM.

HCF(8, 7) × LCM(8, 7) = 8 × 7
Since the HCF of 8 and 7 = 1
⇒ 1 × LCM(8, 7) = 56
Therefore, LCM = 56
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