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GCF of 22 and 33

GCF of 22 and 33 is the largest possible number that divides 22 and 33 exactly without any remainder. The factors of 22 and 33 are 1, 2, 11, 22 and 1, 3, 11, 33 respectively. There are 3 commonly used methods to find the GCF of 22 and 33 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 22 and 33
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 22 and 33?

Answer: GCF of 22 and 33 is 11.

Explanation:

The GCF of two non-zero integers, x(22) and y(33), is the greatest positive integer m(11) that divides both x(22) and y(33) without any remainder.

Methods to Find GCF of 22 and 33

The methods to find the GCF of 22 and 33 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 22 and 33 by Listing Common Factors

Factors of 22: 1, 2, 11, 22
Factors of 33: 1, 3, 11, 33

There are 2 common factors of 22 and 33, that are 1 and 11. Therefore, the greatest common factor of 22 and 33 is 11.

GCF of 22 and 33 by Prime Factorization

Prime factorization of 22 and 33 is (2 × 11) and (3 × 11) respectively. As visible, 22 and 33 have only one common prime factor i.e. 11. Hence, the GCF of 22 and 33 is 11.

GCF of 22 and 33 by Long Division

GCF of 22 and 33 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 33 (larger number) by 22 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (22) by the remainder (11).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (11) is the GCF of 22 and 33.

☛ Also Check:

GCF of 22 and 33 Examples

Example 1: For two numbers, GCF = 11 and LCM = 66. If one number is 22, find the other number.

Solution:

Given: GCF (x, 22) = 11 and LCM (x, 22) = 66
∵ GCF × LCM = 22 × (x)
⇒ x = (GCF × LCM)/22
⇒ x = (11 × 66)/22
⇒ x = 33
Therefore, the other number is 33.
Example 2: Find the GCF of 22 and 33, if their LCM is 66.

Solution:

∵ LCM × GCF = 22 × 33
⇒ GCF(22, 33) = (22 × 33)/66 = 11
Therefore, the greatest common factor of 22 and 33 is 11.
Example 3: Find the greatest number that divides 22 and 33 exactly.

Solution:

The greatest number that divides 22 and 33 exactly is their greatest common factor, i.e. GCF of 22 and 33.
⇒ Factors of 22 and 33:
- Factors of 22 = 1, 2, 11, 22
- Factors of 33 = 1, 3, 11, 33
Therefore, the GCF of 22 and 33 is 11.

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FAQs on GCF of 22 and 33

What is the GCF of 22 and 33?

The GCF of 22 and 33 is 11. To calculate the greatest common factor of 22 and 33, we need to factor each number (factors of 22 = 1, 2, 11, 22; factors of 33 = 1, 3, 11, 33) and choose the greatest factor that exactly divides both 22 and 33, i.e., 11.

How to Find the GCF of 22 and 33 by Prime Factorization?

To find the GCF of 22 and 33, we will find the prime factorization of the given numbers, i.e. 22 = 2 × 11; 33 = 3 × 11.
⇒ Since 11 is the only common prime factor of 22 and 33. Hence, GCF (22, 33) = 11.
☛ Prime Numbers

If the GCF of 33 and 22 is 11, Find its LCM.

GCF(33, 22) × LCM(33, 22) = 33 × 22
Since the GCF of 33 and 22 = 11
⇒ 11 × LCM(33, 22) = 726
Therefore, LCM = 66
☛ GCF Calculator

What are the Methods to Find GCF of 22 and 33?

There are three commonly used methods to find the GCF of 22 and 33.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 22 and 33 by Long Division Method?

To find the GCF of 22, 33 using long division method, 33 is divided by 22. The corresponding divisor (11) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 22, 33?

The following equation can be used to express the relation between LCM and GCF of 22 and 33, i.e. GCF × LCM = 22 × 33.

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