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GCF of 28 and 30

GCF of 28 and 30 is the largest possible number that divides 28 and 30 exactly without any remainder. The factors of 28 and 30 are 1, 2, 4, 7, 14, 28 and 1, 2, 3, 5, 6, 10, 15, 30 respectively. There are 3 commonly used methods to find the GCF of 28 and 30 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 28 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 28 and 30?

Answer: GCF of 28 and 30 is 2.

Explanation:

The GCF of two non-zero integers, x(28) and y(30), is the greatest positive integer m(2) that divides both x(28) and y(30) without any remainder.

Methods to Find GCF of 28 and 30

The methods to find the GCF of 28 and 30 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 28 and 30 by Long Division

GCF of 28 and 30 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 30 (larger number) by 28 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (28) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 28 and 30.

GCF of 28 and 30 by Prime Factorization

Prime factorization of 28 and 30 is (2 × 2 × 7) and (2 × 3 × 5) respectively. As visible, 28 and 30 have only one common prime factor i.e. 2. Hence, the GCF of 28 and 30 is 2.

GCF of 28 and 30 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 = 30 and Y = 28

GCF(30, 28) = GCF(28, 30 mod 28) = GCF(28, 2)
GCF(28, 2) = GCF(2, 28 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 28 and 30 is 2.

☛ Also Check:

GCF of 28 and 30 Examples

Example 1: Find the GCF of 28 and 30, if their LCM is 420.

Solution:

∵ LCM × GCF = 28 × 30
⇒ GCF(28, 30) = (28 × 30)/420 = 2
Therefore, the greatest common factor of 28 and 30 is 2.
Example 2: The product of two numbers is 840. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 840
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 840/2
Therefore, the LCM is 420.
Example 3: Find the greatest number that divides 28 and 30 exactly.

Solution:

The greatest number that divides 28 and 30 exactly is their greatest common factor, i.e. GCF of 28 and 30.
⇒ Factors of 28 and 30:
- Factors of 28 = 1, 2, 4, 7, 14, 28
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Therefore, the GCF of 28 and 30 is 2.

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FAQs on GCF of 28 and 30

What is the GCF of 28 and 30?

The GCF of 28 and 30 is 2. To calculate the greatest common factor of 28 and 30, we need to factor each number (factors of 28 = 1, 2, 4, 7, 14, 28; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the greatest factor that exactly divides both 28 and 30, i.e., 2.

How to Find the GCF of 28 and 30 by Prime Factorization?

To find the GCF of 28 and 30, we will find the prime factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 30 = 2 × 3 × 5.
⇒ Since 2 is the only common prime factor of 28 and 30. Hence, GCF (28, 30) = 2.
☛ Prime Numbers

What is the Relation Between LCM and GCF of 28, 30?

The following equation can be used to express the relation between LCM and GCF of 28 and 30, i.e. GCF × LCM = 28 × 30.

How to Find the GCF of 28 and 30 by Long Division Method?

To find the GCF of 28, 30 using long division method, 30 is divided by 28. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 28 and 30?

There are three commonly used methods to find the GCF of 28 and 30.

By Long Division
By Prime Factorization
By Euclidean Algorithm

If the GCF of 30 and 28 is 2, Find its LCM.

GCF(30, 28) × LCM(30, 28) = 30 × 28
Since the GCF of 30 and 28 = 2
⇒ 2 × LCM(30, 28) = 840
Therefore, LCM = 420
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