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GCF of 28 and 44

GCF of 28 and 44 is the largest possible number that divides 28 and 44 exactly without any remainder. The factors of 28 and 44 are 1, 2, 4, 7, 14, 28 and 1, 2, 4, 11, 22, 44 respectively. There are 3 commonly used methods to find the GCF of 28 and 44 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 28 and 44
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 28 and 44?

Answer: GCF of 28 and 44 is 4.

Explanation:

The GCF of two non-zero integers, x(28) and y(44), is the greatest positive integer m(4) that divides both x(28) and y(44) without any remainder.

Methods to Find GCF of 28 and 44

Let's look at the different methods for finding the GCF of 28 and 44.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 28 and 44 by Long Division

GCF of 28 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 28 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (28) by the remainder (16).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 28 and 44.

GCF of 28 and 44 by Prime Factorization

Prime factorization of 28 and 44 is (2 × 2 × 7) and (2 × 2 × 11) respectively. As visible, 28 and 44 have common prime factors. Hence, the GCF of 28 and 44 is 2 × 2 = 4.

GCF of 28 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 = 28

GCF(44, 28) = GCF(28, 44 mod 28) = GCF(28, 16)
GCF(28, 16) = GCF(16, 28 mod 16) = GCF(16, 12)
GCF(16, 12) = GCF(12, 16 mod 12) = GCF(12, 4)
GCF(12, 4) = GCF(4, 12 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 28 and 44 is 4.

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GCF of 28 and 44 Examples

Example 1: The product of two numbers is 1232. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 1232
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1232/4
Therefore, the LCM is 308.
Example 2: For two numbers, GCF = 4 and LCM = 308. If one number is 44, find the other number.

Solution:

Given: GCF (y, 44) = 4 and LCM (y, 44) = 308
∵ GCF × LCM = 44 × (y)
⇒ y = (GCF × LCM)/44
⇒ y = (4 × 308)/44
⇒ y = 28
Therefore, the other number is 28.
Example 3: Find the greatest number that divides 28 and 44 exactly.

Solution:

The greatest number that divides 28 and 44 exactly is their greatest common factor, i.e. GCF of 28 and 44.
⇒ Factors of 28 and 44:
- Factors of 28 = 1, 2, 4, 7, 14, 28
- Factors of 44 = 1, 2, 4, 11, 22, 44
Therefore, the GCF of 28 and 44 is 4.

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FAQs on GCF of 28 and 44

What is the GCF of 28 and 44?

The GCF of 28 and 44 is 4. To calculate the greatest common factor of 28 and 44, we need to factor each number (factors of 28 = 1, 2, 4, 7, 14, 28; factors of 44 = 1, 2, 4, 11, 22, 44) and choose the greatest factor that exactly divides both 28 and 44, i.e., 4.

How to Find the GCF of 28 and 44 by Long Division Method?

To find the GCF of 28, 44 using long division method, 44 is divided by 28. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 28, 44?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 28 and 44, i.e. GCF × LCM = 28 × 44.

What are the Methods to Find GCF of 28 and 44?

There are three commonly used methods to find the GCF of 28 and 44.

By Prime Factorization
By Long Division
By Euclidean Algorithm

If the GCF of 44 and 28 is 4, Find its LCM.

GCF(44, 28) × LCM(44, 28) = 44 × 28
Since the GCF of 44 and 28 = 4
⇒ 4 × LCM(44, 28) = 1232
Therefore, LCM = 308
☛ Greatest Common Factor Calculator

How to Find the GCF of 28 and 44 by Prime Factorization?

To find the GCF of 28 and 44, we will find the prime factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 44 = 2 × 2 × 11.
⇒ Since 2, 2 are common terms in the prime factorization of 28 and 44. Hence, GCF(28, 44) = 2 × 2 = 4
☛ What are Prime Numbers?

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