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GCF of 8 and 11

GCF of 8 and 11 is the largest possible number that divides 8 and 11 exactly without any remainder. The factors of 8 and 11 are 1, 2, 4, 8 and 1, 11 respectively. There are 3 commonly used methods to find the GCF of 8 and 11 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 8 and 11
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 8 and 11?

Answer: GCF of 8 and 11 is 1.

Explanation:

The GCF of two non-zero integers, x(8) and y(11), is the greatest positive integer m(1) that divides both x(8) and y(11) without any remainder.

Methods to Find GCF of 8 and 11

The methods to find the GCF of 8 and 11 are explained below.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

GCF of 8 and 11 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 11 and Y = 8

GCF(11, 8) = GCF(8, 11 mod 8) = GCF(8, 3)
GCF(8, 3) = GCF(3, 8 mod 3) = GCF(3, 2)
GCF(3, 2) = GCF(2, 3 mod 2) = GCF(2, 1)
GCF(2, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 8 and 11 is 1.

GCF of 8 and 11 by Prime Factorization

Prime factorization of 8 and 11 is (2 × 2 × 2) and (11) respectively. As visible, there are no common prime factors between 8 and 11, i.e. they are coprime. Hence, the GCF of 8 and 11 will be 1.

GCF of 8 and 11 by Long Division

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

The corresponding divisor (1) is the GCF of 8 and 11.

☛ Also Check:

GCF of 8 and 11 Examples

Example 1: For two numbers, GCF = 1 and LCM = 88. If one number is 11, find the other number.

Solution:

Given: GCF (y, 11) = 1 and LCM (y, 11) = 88
∵ GCF × LCM = 11 × (y)
⇒ y = (GCF × LCM)/11
⇒ y = (1 × 88)/11
⇒ y = 8
Therefore, the other number is 8.
Example 2: Find the GCF of 8 and 11, if their LCM is 88.

Solution:

∵ LCM × GCF = 8 × 11
⇒ GCF(8, 11) = (8 × 11)/88 = 1
Therefore, the greatest common factor of 8 and 11 is 1.
Example 3: Find the greatest number that divides 8 and 11 exactly.

Solution:

The greatest number that divides 8 and 11 exactly is their greatest common factor, i.e. GCF of 8 and 11.
⇒ Factors of 8 and 11:
- Factors of 8 = 1, 2, 4, 8
- Factors of 11 = 1, 11
Therefore, the GCF of 8 and 11 is 1.

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FAQs on GCF of 8 and 11

What is the GCF of 8 and 11?

The GCF of 8 and 11 is 1. To calculate the GCF (Greatest Common Factor) of 8 and 11, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 11 = 1, 11) and choose the greatest factor that exactly divides both 8 and 11, i.e., 1.

What is the Relation Between LCM and GCF of 8, 11?

The following equation can be used to express the relation between LCM and GCF of 8 and 11, i.e. GCF × LCM = 8 × 11.

What are the Methods to Find GCF of 8 and 11?

There are three commonly used methods to find the GCF of 8 and 11.

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the GCF of 8 and 11 by Long Division Method?

To find the GCF of 8, 11 using long division method, 11 is divided by 8. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

How to Find the GCF of 8 and 11 by Prime Factorization?

To find the GCF of 8 and 11, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 11 = 11.
⇒ There is no common prime factor for 8 and 11. Hence, GCF (8, 11) = 1.
☛ What are Prime Numbers?

If the GCF of 11 and 8 is 1, Find its LCM.

GCF(11, 8) × LCM(11, 8) = 11 × 8
Since the GCF of 11 and 8 = 1
⇒ 1 × LCM(11, 8) = 88
Therefore, LCM = 88
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