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GCF of 18 and 22

GCF of 18 and 22 is the largest possible number that divides 18 and 22 exactly without any remainder. The factors of 18 and 22 are 1, 2, 3, 6, 9, 18 and 1, 2, 11, 22 respectively. There are 3 commonly used methods to find the GCF of 18 and 22 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 18 and 22
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 18 and 22?

Answer: GCF of 18 and 22 is 2.

Explanation:

The GCF of two non-zero integers, x(18) and y(22), is the greatest positive integer m(2) that divides both x(18) and y(22) without any remainder.

Methods to Find GCF of 18 and 22

The methods to find the GCF of 18 and 22 are explained below.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

GCF of 18 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 = 18

GCF(22, 18) = GCF(18, 22 mod 18) = GCF(18, 4)
GCF(18, 4) = GCF(4, 18 mod 4) = GCF(4, 2)
GCF(4, 2) = GCF(2, 4 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 18 and 22 is 2.

GCF of 18 and 22 by Prime Factorization

Prime factorization of 18 and 22 is (2 × 3 × 3) and (2 × 11) respectively. As visible, 18 and 22 have only one common prime factor i.e. 2. Hence, the GCF of 18 and 22 is 2.

GCF of 18 and 22 by Long Division

GCF of 18 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 18 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 18 and 22.

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GCF of 18 and 22 Examples

Example 1: The product of two numbers is 396. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 396
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 396/2
Therefore, the LCM is 198.
Example 2: Find the greatest number that divides 18 and 22 exactly.

Solution:

The greatest number that divides 18 and 22 exactly is their greatest common factor, i.e. GCF of 18 and 22.
⇒ Factors of 18 and 22:
- Factors of 18 = 1, 2, 3, 6, 9, 18
- Factors of 22 = 1, 2, 11, 22
Therefore, the GCF of 18 and 22 is 2.
Example 3: Find the GCF of 18 and 22, if their LCM is 198.

Solution:

∵ LCM × GCF = 18 × 22
⇒ GCF(18, 22) = (18 × 22)/198 = 2
Therefore, the greatest common factor of 18 and 22 is 2.

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FAQs on GCF of 18 and 22

What is the GCF of 18 and 22?

The GCF of 18 and 22 is 2. To calculate the greatest common factor of 18 and 22, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 22 = 1, 2, 11, 22) and choose the greatest factor that exactly divides both 18 and 22, i.e., 2.

If the GCF of 22 and 18 is 2, Find its LCM.

GCF(22, 18) × LCM(22, 18) = 22 × 18
Since the GCF of 22 and 18 = 2
⇒ 2 × LCM(22, 18) = 396
Therefore, LCM = 198
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What are the Methods to Find GCF of 18 and 22?

There are three commonly used methods to find the GCF of 18 and 22.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the GCF of 18 and 22 by Long Division Method?

To find the GCF of 18, 22 using long division method, 22 is divided by 18. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 18, 22?

The following equation can be used to express the relation between Least Common Multiple and GCF of 18 and 22, i.e. GCF × LCM = 18 × 22.

How to Find the GCF of 18 and 22 by Prime Factorization?

To find the GCF of 18 and 22, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 22 = 2 × 11.
⇒ Since 2 is the only common prime factor of 18 and 22. Hence, GCF (18, 22) = 2.
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