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GCF of 22 and 44

GCF of 22 and 44 is the largest possible number that divides 22 and 44 exactly without any remainder. The factors of 22 and 44 are 1, 2, 11, 22 and 1, 2, 4, 11, 22, 44 respectively. There are 3 commonly used methods to find the GCF of 22 and 44 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 22 and 44
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 22 and 44?

Answer: GCF of 22 and 44 is 22.

Explanation:

The GCF of two non-zero integers, x(22) and y(44), is the greatest positive integer m(22) that divides both x(22) and y(44) without any remainder.

Methods to Find GCF of 22 and 44

The methods to find the GCF of 22 and 44 are explained below.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

GCF of 22 and 44 by Listing Common Factors

Factors of 22: 1, 2, 11, 22
Factors of 44: 1, 2, 4, 11, 22, 44

There are 4 common factors of 22 and 44, that are 1, 2, 11, and 22. Therefore, the greatest common factor of 22 and 44 is 22.

GCF of 22 and 44 by Prime Factorization

Prime factorization of 22 and 44 is (2 × 11) and (2 × 2 × 11) respectively. As visible, 22 and 44 have common prime factors. Hence, the GCF of 22 and 44 is 2 × 11 = 22.

GCF of 22 and 44 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 = 44 and Y = 22

GCF(44, 22) = GCF(22, 44 mod 22) = GCF(22, 0)
GCF(22, 0) = 22 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 22 and 44 is 22.

☛ Also Check:

GCF of 22 and 44 Examples

Example 1: Find the greatest number that divides 22 and 44 exactly.

Solution:

The greatest number that divides 22 and 44 exactly is their greatest common factor, i.e. GCF of 22 and 44.
⇒ Factors of 22 and 44:
- Factors of 22 = 1, 2, 11, 22
- Factors of 44 = 1, 2, 4, 11, 22, 44
Therefore, the GCF of 22 and 44 is 22.
Example 2: The product of two numbers is 968. If their GCF is 22, what is their LCM?

Solution:

Given: GCF = 22 and product of numbers = 968
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 968/22
Therefore, the LCM is 44.
Example 3: Find the GCF of 22 and 44, if their LCM is 44.

Solution:

∵ LCM × GCF = 22 × 44
⇒ GCF(22, 44) = (22 × 44)/44 = 22
Therefore, the greatest common factor of 22 and 44 is 22.

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FAQs on GCF of 22 and 44

What is the GCF of 22 and 44?

The GCF of 22 and 44 is 22. To calculate the greatest common factor of 22 and 44, we need to factor each number (factors of 22 = 1, 2, 11, 22; factors of 44 = 1, 2, 4, 11, 22, 44) and choose the greatest factor that exactly divides both 22 and 44, i.e., 22.

How to Find the GCF of 22 and 44 by Long Division Method?

To find the GCF of 22, 44 using long division method, 44 is divided by 22. The corresponding divisor (22) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 22, 44?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 22 and 44, i.e. GCF × LCM = 22 × 44.

How to Find the GCF of 22 and 44 by Prime Factorization?

To find the GCF of 22 and 44, we will find the prime factorization of the given numbers, i.e. 22 = 2 × 11; 44 = 2 × 2 × 11.
⇒ Since 2, 11 are common terms in the prime factorization of 22 and 44. Hence, GCF(22, 44) = 2 × 11 = 22
☛ Prime Number

What are the Methods to Find GCF of 22 and 44?

There are three commonly used methods to find the GCF of 22 and 44.

By Long Division
By Prime Factorization
By Euclidean Algorithm

If the GCF of 44 and 22 is 22, Find its LCM.

GCF(44, 22) × LCM(44, 22) = 44 × 22
Since the GCF of 44 and 22 = 22
⇒ 22 × LCM(44, 22) = 968
Therefore, LCM = 44
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