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GCF of 33 and 44

GCF of 33 and 44 is the largest possible number that divides 33 and 44 exactly without any remainder. The factors of 33 and 44 are 1, 3, 11, 33 and 1, 2, 4, 11, 22, 44 respectively. There are 3 commonly used methods to find the GCF of 33 and 44 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 33 and 44
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 33 and 44?

Answer: GCF of 33 and 44 is 11.

Explanation:

The GCF of two non-zero integers, x(33) and y(44), is the greatest positive integer m(11) that divides both x(33) and y(44) without any remainder.

Methods to Find GCF of 33 and 44

Let's look at the different methods for finding the GCF of 33 and 44.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 33 and 44 by Listing Common Factors

Factors of 33: 1, 3, 11, 33
Factors of 44: 1, 2, 4, 11, 22, 44

There are 2 common factors of 33 and 44, that are 1 and 11. Therefore, the greatest common factor of 33 and 44 is 11.

GCF of 33 and 44 by Prime Factorization

Prime factorization of 33 and 44 is (3 × 11) and (2 × 2 × 11) respectively. As visible, 33 and 44 have only one common prime factor i.e. 11. Hence, the GCF of 33 and 44 is 11.

GCF of 33 and 44 by Long Division

GCF of 33 and 44 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 44 (larger number) by 33 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (33) by the remainder (11).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (11) is the GCF of 33 and 44.

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GCF of 33 and 44 Examples

Example 1: Find the greatest number that divides 33 and 44 exactly.

Solution:

The greatest number that divides 33 and 44 exactly is their greatest common factor, i.e. GCF of 33 and 44.
⇒ Factors of 33 and 44:
- Factors of 33 = 1, 3, 11, 33
- Factors of 44 = 1, 2, 4, 11, 22, 44
Therefore, the GCF of 33 and 44 is 11.
Example 2: Find the GCF of 33 and 44, if their LCM is 132.

Solution:

∵ LCM × GCF = 33 × 44
⇒ GCF(33, 44) = (33 × 44)/132 = 11
Therefore, the greatest common factor of 33 and 44 is 11.
Example 3: For two numbers, GCF = 11 and LCM = 132. If one number is 33, find the other number.

Solution:

Given: GCF (x, 33) = 11 and LCM (x, 33) = 132
∵ GCF × LCM = 33 × (x)
⇒ x = (GCF × LCM)/33
⇒ x = (11 × 132)/33
⇒ x = 44
Therefore, the other number is 44.

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FAQs on GCF of 33 and 44

What is the GCF of 33 and 44?

The GCF of 33 and 44 is 11. To calculate the GCF of 33 and 44, we need to factor each number (factors of 33 = 1, 3, 11, 33; factors of 44 = 1, 2, 4, 11, 22, 44) and choose the greatest factor that exactly divides both 33 and 44, i.e., 11.

How to Find the GCF of 33 and 44 by Prime Factorization?

To find the GCF of 33 and 44, we will find the prime factorization of the given numbers, i.e. 33 = 3 × 11; 44 = 2 × 2 × 11.
⇒ Since 11 is the only common prime factor of 33 and 44. Hence, GCF (33, 44) = 11.
☛ What are Prime Numbers?

What are the Methods to Find GCF of 33 and 44?

There are three commonly used methods to find the GCF of 33 and 44.

By Long Division
By Prime Factorization
By Euclidean Algorithm

What is the Relation Between LCM and GCF of 33, 44?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 33 and 44, i.e. GCF × LCM = 33 × 44.

If the GCF of 44 and 33 is 11, Find its LCM.

GCF(44, 33) × LCM(44, 33) = 44 × 33
Since the GCF of 44 and 33 = 11
⇒ 11 × LCM(44, 33) = 1452
Therefore, LCM = 132
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How to Find the GCF of 33 and 44 by Long Division Method?

To find the GCF of 33, 44 using long division method, 44 is divided by 33. The corresponding divisor (11) when remainder equals 0 is taken as GCF.

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