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GCF of 11 and 22

GCF of 11 and 22 is the largest possible number that divides 11 and 22 exactly without any remainder. The factors of 11 and 22 are 1, 11 and 1, 2, 11, 22 respectively. There are 3 commonly used methods to find the GCF of 11 and 22 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 11 and 22
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 11 and 22?

Answer: GCF of 11 and 22 is 11.

Explanation:

The GCF of two non-zero integers, x(11) and y(22), is the greatest positive integer m(11) that divides both x(11) and y(22) without any remainder.

Methods to Find GCF of 11 and 22

Let's look at the different methods for finding the GCF of 11 and 22.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 11 and 22 by Prime Factorization

Prime factorization of 11 and 22 is (11) and (2 × 11) respectively. As visible, 11 and 22 have only one common prime factor i.e. 11. Hence, the GCF of 11 and 22 is 11.

GCF of 11 and 22 by Listing Common Factors

Factors of 11: 1, 11
Factors of 22: 1, 2, 11, 22

There are 2 common factors of 11 and 22, that are 1 and 11. Therefore, the greatest common factor of 11 and 22 is 11.

GCF of 11 and 22 by Long Division

GCF of 11 and 22 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 22 (larger number) by 11 (smaller number).
Step 2: Since the remainder = 0, the divisor (11) is the GCF of 11 and 22.

The corresponding divisor (11) is the GCF of 11 and 22.

☛ Also Check:

GCF of 11 and 22 Examples

Example 1: For two numbers, GCF = 11 and LCM = 22. If one number is 11, find the other number.

Solution:

Given: GCF (x, 11) = 11 and LCM (x, 11) = 22
∵ GCF × LCM = 11 × (x)
⇒ x = (GCF × LCM)/11
⇒ x = (11 × 22)/11
⇒ x = 22
Therefore, the other number is 22.
Example 2: Find the GCF of 11 and 22, if their LCM is 22.

Solution:

∵ LCM × GCF = 11 × 22
⇒ GCF(11, 22) = (11 × 22)/22 = 11
Therefore, the greatest common factor of 11 and 22 is 11.
Example 3: Find the greatest number that divides 11 and 22 exactly.

Solution:

The greatest number that divides 11 and 22 exactly is their greatest common factor, i.e. GCF of 11 and 22.
⇒ Factors of 11 and 22:
- Factors of 11 = 1, 11
- Factors of 22 = 1, 2, 11, 22
Therefore, the GCF of 11 and 22 is 11.

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FAQs on GCF of 11 and 22

What is the GCF of 11 and 22?

The GCF of 11 and 22 is 11. To calculate the greatest common factor of 11 and 22, we need to factor each number (factors of 11 = 1, 11; factors of 22 = 1, 2, 11, 22) and choose the greatest factor that exactly divides both 11 and 22, i.e., 11.

What is the Relation Between LCM and GCF of 11, 22?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 11 and 22, i.e. GCF × LCM = 11 × 22.

How to Find the GCF of 11 and 22 by Long Division Method?

To find the GCF of 11, 22 using long division method, 22 is divided by 11. The corresponding divisor (11) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 11 and 22?

There are three commonly used methods to find the GCF of 11 and 22.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 11 and 22 by Prime Factorization?

To find the GCF of 11 and 22, we will find the prime factorization of the given numbers, i.e. 11 = 11; 22 = 2 × 11.
⇒ Since 11 is the only common prime factor of 11 and 22. Hence, GCF (11, 22) = 11.
☛ Prime Number

If the GCF of 22 and 11 is 11, Find its LCM.

GCF(22, 11) × LCM(22, 11) = 22 × 11
Since the GCF of 22 and 11 = 11
⇒ 11 × LCM(22, 11) = 242
Therefore, LCM = 22
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