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GCF of 20 and 22

GCF of 20 and 22 is the largest possible number that divides 20 and 22 exactly without any remainder. The factors of 20 and 22 are 1, 2, 4, 5, 10, 20 and 1, 2, 11, 22 respectively. There are 3 commonly used methods to find the GCF of 20 and 22 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 20 and 22
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 20 and 22?

Answer: GCF of 20 and 22 is 2.

Explanation:

The GCF of two non-zero integers, x(20) and y(22), is the greatest positive integer m(2) that divides both x(20) and y(22) without any remainder.

Methods to Find GCF of 20 and 22

Let's look at the different methods for finding the GCF of 20 and 22.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 20 and 22 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 = 22 and Y = 20

GCF(22, 20) = GCF(20, 22 mod 20) = GCF(20, 2)
GCF(20, 2) = GCF(2, 20 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 20 and 22 is 2.

GCF of 20 and 22 by Long Division

GCF of 20 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 20 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 20 and 22.

GCF of 20 and 22 by Listing Common Factors

Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 22: 1, 2, 11, 22

There are 2 common factors of 20 and 22, that are 1 and 2. Therefore, the greatest common factor of 20 and 22 is 2.

☛ Also Check:

GCF of 20 and 22 Examples

Example 1: Find the greatest number that divides 20 and 22 exactly.

Solution:

The greatest number that divides 20 and 22 exactly is their greatest common factor, i.e. GCF of 20 and 22.
⇒ Factors of 20 and 22:
- Factors of 20 = 1, 2, 4, 5, 10, 20
- Factors of 22 = 1, 2, 11, 22
Therefore, the GCF of 20 and 22 is 2.
Example 2: The product of two numbers is 440. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 440
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 440/2
Therefore, the LCM is 220.
Example 3: Find the GCF of 20 and 22, if their LCM is 220.

Solution:

∵ LCM × GCF = 20 × 22
⇒ GCF(20, 22) = (20 × 22)/220 = 2
Therefore, the greatest common factor of 20 and 22 is 2.

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FAQs on GCF of 20 and 22

What is the GCF of 20 and 22?

The GCF of 20 and 22 is 2. To calculate the greatest common factor (GCF) of 20 and 22, we need to factor each number (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 22 = 1, 2, 11, 22) and choose the greatest factor that exactly divides both 20 and 22, i.e., 2.

If the GCF of 22 and 20 is 2, Find its LCM.

GCF(22, 20) × LCM(22, 20) = 22 × 20
Since the GCF of 22 and 20 = 2
⇒ 2 × LCM(22, 20) = 440
Therefore, LCM = 220
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How to Find the GCF of 20 and 22 by Long Division Method?

To find the GCF of 20, 22 using long division method, 22 is divided by 20. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 20 and 22?

There are three commonly used methods to find the GCF of 20 and 22.

By Prime Factorization
By Listing Common Factors
By Long Division

What is the Relation Between LCM and GCF of 20, 22?

The following equation can be used to express the relation between Least Common Multiple and GCF of 20 and 22, i.e. GCF × LCM = 20 × 22.

How to Find the GCF of 20 and 22 by Prime Factorization?

To find the GCF of 20 and 22, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 22 = 2 × 11.
⇒ Since 2 is the only common prime factor of 20 and 22. Hence, GCF (20, 22) = 2.
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