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GCF of 44 and 55

GCF of 44 and 55 is the largest possible number that divides 44 and 55 exactly without any remainder. The factors of 44 and 55 are 1, 2, 4, 11, 22, 44 and 1, 5, 11, 55 respectively. There are 3 commonly used methods to find the GCF of 44 and 55 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 44 and 55
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 44 and 55?

Answer: GCF of 44 and 55 is 11.

Explanation:

The GCF of two non-zero integers, x(44) and y(55), is the greatest positive integer m(11) that divides both x(44) and y(55) without any remainder.

Methods to Find GCF of 44 and 55

The methods to find the GCF of 44 and 55 are explained below.

Listing Common Factors
Long Division Method
Using Euclid's Algorithm

GCF of 44 and 55 by Listing Common Factors

Factors of 44: 1, 2, 4, 11, 22, 44
Factors of 55: 1, 5, 11, 55

There are 2 common factors of 44 and 55, that are 1 and 11. Therefore, the greatest common factor of 44 and 55 is 11.

GCF of 44 and 55 by Long Division

GCF of 44 and 55 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 55 (larger number) by 44 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (44) by the remainder (11).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (11) is the GCF of 44 and 55.

GCF of 44 and 55 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 = 55 and Y = 44

GCF(55, 44) = GCF(44, 55 mod 44) = GCF(44, 11)
GCF(44, 11) = GCF(11, 44 mod 11) = GCF(11, 0)
GCF(11, 0) = 11 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 44 and 55 is 11.

☛ Also Check:

GCF of 44 and 55 Examples

Example 1: Find the greatest number that divides 44 and 55 exactly.

Solution:

The greatest number that divides 44 and 55 exactly is their greatest common factor, i.e. GCF of 44 and 55.
⇒ Factors of 44 and 55:
- Factors of 44 = 1, 2, 4, 11, 22, 44
- Factors of 55 = 1, 5, 11, 55
Therefore, the GCF of 44 and 55 is 11.
Example 2: Find the GCF of 44 and 55, if their LCM is 220.

Solution:

∵ LCM × GCF = 44 × 55
⇒ GCF(44, 55) = (44 × 55)/220 = 11
Therefore, the greatest common factor of 44 and 55 is 11.
Example 3: For two numbers, GCF = 11 and LCM = 220. If one number is 44, find the other number.

Solution:

Given: GCF (z, 44) = 11 and LCM (z, 44) = 220
∵ GCF × LCM = 44 × (z)
⇒ z = (GCF × LCM)/44
⇒ z = (11 × 220)/44
⇒ z = 55
Therefore, the other number is 55.

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FAQs on GCF of 44 and 55

What is the GCF of 44 and 55?

The GCF of 44 and 55 is 11. To calculate the GCF of 44 and 55, we need to factor each number (factors of 44 = 1, 2, 4, 11, 22, 44; factors of 55 = 1, 5, 11, 55) and choose the greatest factor that exactly divides both 44 and 55, i.e., 11.

How to Find the GCF of 44 and 55 by Long Division Method?

To find the GCF of 44, 55 using long division method, 55 is divided by 44. The corresponding divisor (11) when remainder equals 0 is taken as GCF.

How to Find the GCF of 44 and 55 by Prime Factorization?

To find the GCF of 44 and 55, we will find the prime factorization of the given numbers, i.e. 44 = 2 × 2 × 11; 55 = 5 × 11.
⇒ Since 11 is the only common prime factor of 44 and 55. Hence, GCF (44, 55) = 11.
☛ Prime Numbers

If the GCF of 55 and 44 is 11, Find its LCM.

GCF(55, 44) × LCM(55, 44) = 55 × 44
Since the GCF of 55 and 44 = 11
⇒ 11 × LCM(55, 44) = 2420
Therefore, LCM = 220
☛ GCF Calculator

What is the Relation Between LCM and GCF of 44, 55?

The following equation can be used to express the relation between Least Common Multiple and GCF of 44 and 55, i.e. GCF × LCM = 44 × 55.

What are the Methods to Find GCF of 44 and 55?

There are three commonly used methods to find the GCF of 44 and 55.

By Long Division
By Prime Factorization
By Listing Common Factors

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