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GCF of 24 and 44

GCF of 24 and 44 is the largest possible number that divides 24 and 44 exactly without any remainder. The factors of 24 and 44 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 4, 11, 22, 44 respectively. There are 3 commonly used methods to find the GCF of 24 and 44 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 24 and 44
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 44?

Answer: GCF of 24 and 44 is 4.

Explanation:

The GCF of two non-zero integers, x(24) and y(44), is the greatest positive integer m(4) that divides both x(24) and y(44) without any remainder.

Methods to Find GCF of 24 and 44

Let's look at the different methods for finding the GCF of 24 and 44.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 24 and 44 by Long Division

GCF of 24 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 24 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (20).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 24 and 44.

GCF of 24 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 = 24

GCF(44, 24) = GCF(24, 44 mod 24) = GCF(24, 20)
GCF(24, 20) = GCF(20, 24 mod 20) = GCF(20, 4)
GCF(20, 4) = GCF(4, 20 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 24 and 44 is 4.

GCF of 24 and 44 by Listing Common Factors

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 44: 1, 2, 4, 11, 22, 44

There are 3 common factors of 24 and 44, that are 1, 2, and 4. Therefore, the greatest common factor of 24 and 44 is 4.

☛ Also Check:

GCF of 24 and 44 Examples

Example 1: Find the greatest number that divides 24 and 44 exactly.

Solution:

The greatest number that divides 24 and 44 exactly is their greatest common factor, i.e. GCF of 24 and 44.
⇒ Factors of 24 and 44:
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 44 = 1, 2, 4, 11, 22, 44
Therefore, the GCF of 24 and 44 is 4.
Example 2: Find the GCF of 24 and 44, if their LCM is 264.

Solution:

∵ LCM × GCF = 24 × 44
⇒ GCF(24, 44) = (24 × 44)/264 = 4
Therefore, the greatest common factor of 24 and 44 is 4.
Example 3: The product of two numbers is 1056. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 1056
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1056/4
Therefore, the LCM is 264.

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FAQs on GCF of 24 and 44

What is the GCF of 24 and 44?

The GCF of 24 and 44 is 4. To calculate the greatest common factor (GCF) of 24 and 44, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 44 = 1, 2, 4, 11, 22, 44) and choose the greatest factor that exactly divides both 24 and 44, i.e., 4.

What are the Methods to Find GCF of 24 and 44?

There are three commonly used methods to find the GCF of 24 and 44.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the GCF of 24 and 44 by Prime Factorization?

To find the GCF of 24 and 44, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 44 = 2 × 2 × 11.
⇒ Since 2, 2 are common terms in the prime factorization of 24 and 44. Hence, GCF(24, 44) = 2 × 2 = 4
☛ What is a Prime Number?

How to Find the GCF of 24 and 44 by Long Division Method?

To find the GCF of 24, 44 using long division method, 44 is divided by 24. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 24, 44?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 24 and 44, i.e. GCF × LCM = 24 × 44.

If the GCF of 44 and 24 is 4, Find its LCM.

GCF(44, 24) × LCM(44, 24) = 44 × 24
Since the GCF of 44 and 24 = 4
⇒ 4 × LCM(44, 24) = 1056
Therefore, LCM = 264
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