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GCF of 28 and 56

GCF of 28 and 56 is the largest possible number that divides 28 and 56 exactly without any remainder. The factors of 28 and 56 are 1, 2, 4, 7, 14, 28 and 1, 2, 4, 7, 8, 14, 28, 56 respectively. There are 3 commonly used methods to find the GCF of 28 and 56 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 28 and 56
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 28 and 56?

Answer: GCF of 28 and 56 is 28.

Explanation:

The GCF of two non-zero integers, x(28) and y(56), is the greatest positive integer m(28) that divides both x(28) and y(56) without any remainder.

Methods to Find GCF of 28 and 56

The methods to find the GCF of 28 and 56 are explained below.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 28 and 56 by Long Division

GCF of 28 and 56 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 56 (larger number) by 28 (smaller number).
Step 2: Since the remainder = 0, the divisor (28) is the GCF of 28 and 56.

The corresponding divisor (28) is the GCF of 28 and 56.

GCF of 28 and 56 by Listing Common Factors

Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56

There are 6 common factors of 28 and 56, that are 1, 2, 4, 7, 14, and 28. Therefore, the greatest common factor of 28 and 56 is 28.

GCF of 28 and 56 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 = 56 and Y = 28

GCF(56, 28) = GCF(28, 56 mod 28) = GCF(28, 0)
GCF(28, 0) = 28 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 28 and 56 is 28.

☛ Also Check:

GCF of 28 and 56 Examples

Example 1: The product of two numbers is 1568. If their GCF is 28, what is their LCM?

Solution:

Given: GCF = 28 and product of numbers = 1568
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1568/28
Therefore, the LCM is 56.
Example 2: Find the greatest number that divides 28 and 56 exactly.

Solution:

The greatest number that divides 28 and 56 exactly is their greatest common factor, i.e. GCF of 28 and 56.
⇒ Factors of 28 and 56:
- Factors of 28 = 1, 2, 4, 7, 14, 28
- Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
Therefore, the GCF of 28 and 56 is 28.
Example 3: Find the GCF of 28 and 56, if their LCM is 56.

Solution:

∵ LCM × GCF = 28 × 56
⇒ GCF(28, 56) = (28 × 56)/56 = 28
Therefore, the greatest common factor of 28 and 56 is 28.

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FAQs on GCF of 28 and 56

What is the GCF of 28 and 56?

The GCF of 28 and 56 is 28. To calculate the greatest common factor (GCF) of 28 and 56, we need to factor each number (factors of 28 = 1, 2, 4, 7, 14, 28; factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56) and choose the greatest factor that exactly divides both 28 and 56, i.e., 28.

If the GCF of 56 and 28 is 28, Find its LCM.

GCF(56, 28) × LCM(56, 28) = 56 × 28
Since the GCF of 56 and 28 = 28
⇒ 28 × LCM(56, 28) = 1568
Therefore, LCM = 56
☛ GCF Calculator

What is the Relation Between LCM and GCF of 28, 56?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 28 and 56, i.e. GCF × LCM = 28 × 56.

How to Find the GCF of 28 and 56 by Prime Factorization?

To find the GCF of 28 and 56, we will find the prime factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 56 = 2 × 2 × 2 × 7.
⇒ Since 2, 2, 7 are common terms in the prime factorization of 28 and 56. Hence, GCF(28, 56) = 2 × 2 × 7 = 28
☛ What are Prime Numbers?

How to Find the GCF of 28 and 56 by Long Division Method?

To find the GCF of 28, 56 using long division method, 56 is divided by 28. The corresponding divisor (28) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 28 and 56?

There are three commonly used methods to find the GCF of 28 and 56.

By Prime Factorization
By Euclidean Algorithm
By Long Division

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