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GCF of 36 and 44

GCF of 36 and 44 is the largest possible number that divides 36 and 44 exactly without any remainder. The factors of 36 and 44 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 4, 11, 22, 44 respectively. There are 3 commonly used methods to find the GCF of 36 and 44 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 36 and 44
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 36 and 44?

Answer: GCF of 36 and 44 is 4.

Explanation:

The GCF of two non-zero integers, x(36) and y(44), is the greatest positive integer m(4) that divides both x(36) and y(44) without any remainder.

Methods to Find GCF of 36 and 44

The methods to find the GCF of 36 and 44 are explained below.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 36 and 44 by Long Division

GCF of 36 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 36 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (8).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 36 and 44.

GCF of 36 and 44 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 44: 1, 2, 4, 11, 22, 44

There are 3 common factors of 36 and 44, that are 1, 2, and 4. Therefore, the greatest common factor of 36 and 44 is 4.

GCF of 36 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 = 36

GCF(44, 36) = GCF(36, 44 mod 36) = GCF(36, 8)
GCF(36, 8) = GCF(8, 36 mod 8) = GCF(8, 4)
GCF(8, 4) = GCF(4, 8 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 36 and 44 is 4.

☛ Also Check:

GCF of 36 and 44 Examples

Example 1: For two numbers, GCF = 4 and LCM = 396. If one number is 44, find the other number.

Solution:

Given: GCF (z, 44) = 4 and LCM (z, 44) = 396
∵ GCF × LCM = 44 × (z)
⇒ z = (GCF × LCM)/44
⇒ z = (4 × 396)/44
⇒ z = 36
Therefore, the other number is 36.
Example 2: Find the greatest number that divides 36 and 44 exactly.

Solution:

The greatest number that divides 36 and 44 exactly is their greatest common factor, i.e. GCF of 36 and 44.
⇒ Factors of 36 and 44:
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 44 = 1, 2, 4, 11, 22, 44
Therefore, the GCF of 36 and 44 is 4.
Example 3: The product of two numbers is 1584. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 1584
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1584/4
Therefore, the LCM is 396.

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FAQs on GCF of 36 and 44

What is the GCF of 36 and 44?

The GCF of 36 and 44 is 4. To calculate the GCF (Greatest Common Factor) of 36 and 44, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 44 = 1, 2, 4, 11, 22, 44) and choose the greatest factor that exactly divides both 36 and 44, i.e., 4.

How to Find the GCF of 36 and 44 by Prime Factorization?

To find the GCF of 36 and 44, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 44 = 2 × 2 × 11.
⇒ Since 2, 2 are common terms in the prime factorization of 36 and 44. Hence, GCF(36, 44) = 2 × 2 = 4
☛ Prime Number

How to Find the GCF of 36 and 44 by Long Division Method?

To find the GCF of 36, 44 using long division method, 44 is divided by 36. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 36 and 44?

There are three commonly used methods to find the GCF of 36 and 44.

By Long Division
By Prime Factorization
By Euclidean Algorithm

If the GCF of 44 and 36 is 4, Find its LCM.

GCF(44, 36) × LCM(44, 36) = 44 × 36
Since the GCF of 44 and 36 = 4
⇒ 4 × LCM(44, 36) = 1584
Therefore, LCM = 396
☛ GCF Calculator

What is the Relation Between LCM and GCF of 36, 44?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 36 and 44, i.e. GCF × LCM = 36 × 44.

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