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GCF of 4 and 28

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

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

What is GCF of 4 and 28?

Answer: GCF of 4 and 28 is 4.

Explanation:

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

Methods to Find GCF of 4 and 28

Let's look at the different methods for finding the GCF of 4 and 28.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

GCF of 4 and 28 by Listing Common Factors

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

There are 3 common factors of 4 and 28, that are 1, 2, and 4. Therefore, the greatest common factor of 4 and 28 is 4.

GCF of 4 and 28 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 = 28 and Y = 4

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

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

GCF of 4 and 28 by Long Division

GCF of 4 and 28 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 28 (larger number) by 4 (smaller number).
Step 2: Since the remainder = 0, the divisor (4) is the GCF of 4 and 28.

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

☛ Also Check:

GCF of 4 and 28 Examples

Example 1: Find the greatest number that divides 4 and 28 exactly.

Solution:

The greatest number that divides 4 and 28 exactly is their greatest common factor, i.e. GCF of 4 and 28.
⇒ Factors of 4 and 28:
- Factors of 4 = 1, 2, 4
- Factors of 28 = 1, 2, 4, 7, 14, 28
Therefore, the GCF of 4 and 28 is 4.
Example 2: For two numbers, GCF = 4 and LCM = 28. If one number is 28, find the other number.

Solution:

Given: GCF (z, 28) = 4 and LCM (z, 28) = 28
∵ GCF × LCM = 28 × (z)
⇒ z = (GCF × LCM)/28
⇒ z = (4 × 28)/28
⇒ z = 4
Therefore, the other number is 4.
Example 3: The product of two numbers is 112. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 112
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 112/4
Therefore, the LCM is 28.

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FAQs on GCF of 4 and 28

What is the GCF of 4 and 28?

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

How to Find the GCF of 4 and 28 by Long Division Method?

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

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

GCF(28, 4) × LCM(28, 4) = 28 × 4
Since the GCF of 28 and 4 = 4
⇒ 4 × LCM(28, 4) = 112
Therefore, LCM = 28
☛ GCF Calculator

What are the Methods to Find GCF of 4 and 28?

There are three commonly used methods to find the GCF of 4 and 28.

By Long Division
By Listing Common Factors
By Prime Factorization

How to Find the GCF of 4 and 28 by Prime Factorization?

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

What is the Relation Between LCM and GCF of 4, 28?

The following equation can be used to express the relation between Least Common Multiple and GCF of 4 and 28, i.e. GCF × LCM = 4 × 28.

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