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HCF of 7 and 11

HCF of 7 and 11 is the largest possible number that divides 7 and 11 exactly without any remainder. The factors of 7 and 11 are 1, 7 and 1, 11 respectively. There are 3 commonly used methods to find the HCF of 7 and 11 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 7 and 11
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 7 and 11?

Answer: HCF of 7 and 11 is 1.

Explanation:

The HCF of two non-zero integers, x(7) and y(11), is the highest positive integer m(1) that divides both x(7) and y(11) without any remainder.

Methods to Find HCF of 7 and 11

Let's look at the different methods for finding the HCF of 7 and 11.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

HCF of 7 and 11 by Long Division

HCF of 7 and 11 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 11 (larger number) by 7 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (7) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the HCF of 7 and 11.

HCF of 7 and 11 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 = 11 and Y = 7

HCF(11, 7) = HCF(7, 11 mod 7) = HCF(7, 4)
HCF(7, 4) = HCF(4, 7 mod 4) = HCF(4, 3)
HCF(4, 3) = HCF(3, 4 mod 3) = HCF(3, 1)
HCF(3, 1) = 1 (∵ HCF(X, 1) = 1)

Therefore, the value of HCF of 7 and 11 is 1.

HCF of 7 and 11 by Listing Common Factors

Factors of 7: 1, 7
Factors of 11: 1, 11

Since, 1 is the only common factor between 7 and 11. The highest common factor of 7 and 11 is 1.

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HCF of 7 and 11 Examples

Example 1: The product of two numbers is 77. If their HCF is 1, what is their LCM?

Solution:

Given: HCF = 1 and product of numbers = 77
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 77/1
Therefore, the LCM is 77.
Example 2: Find the HCF of 7 and 11, if their LCM is 77.

Solution:

∵ LCM × HCF = 7 × 11
⇒ HCF(7, 11) = (7 × 11)/77 = 1
Therefore, the highest common factor of 7 and 11 is 1.
Example 3: For two numbers, HCF = 1 and LCM = 77. If one number is 11, find the other number.

Solution:

Given: HCF (z, 11) = 1 and LCM (z, 11) = 77
∵ HCF × LCM = 11 × (z)
⇒ z = (HCF × LCM)/11
⇒ z = (1 × 77)/11
⇒ z = 7
Therefore, the other number is 7.

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FAQs on HCF of 7 and 11

What is the HCF of 7 and 11?

The HCF of 7 and 11 is 1. To calculate the Highest common factor (HCF) of 7 and 11, we need to factor each number (factors of 7 = 1, 7; factors of 11 = 1, 11) and choose the highest factor that exactly divides both 7 and 11, i.e., 1.

What are the Methods to Find HCF of 7 and 11?

There are three commonly used methods to find the HCF of 7 and 11.

By Long Division
By Euclidean Algorithm
By Prime Factorization

What is the Relation Between LCM and HCF of 7, 11?

The following equation can be used to express the relation between Least Common Multiple and HCF of 7 and 11, i.e. HCF × LCM = 7 × 11.

If the HCF of 11 and 7 is 1, Find its LCM.

HCF(11, 7) × LCM(11, 7) = 11 × 7
Since the HCF of 11 and 7 = 1
⇒ 1 × LCM(11, 7) = 77
Therefore, LCM = 77
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How to Find the HCF of 7 and 11 by Long Division Method?

To find the HCF of 7, 11 using long division method, 11 is divided by 7. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

How to Find the HCF of 7 and 11 by Prime Factorization?

To find the HCF of 7 and 11, we will find the prime factorization of the given numbers, i.e. 7 = 7; 11 = 11.
⇒ There is no common prime factor for 7 and 11. Hence, HCF (7, 11) = 1.
☛ What are Prime Numbers?

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