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GCF of 18 and 28

GCF of 18 and 28 is the largest possible number that divides 18 and 28 exactly without any remainder. The factors of 18 and 28 are 1, 2, 3, 6, 9, 18 and 1, 2, 4, 7, 14, 28 respectively. There are 3 commonly used methods to find the GCF of 18 and 28 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 18 and 28
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 18 and 28?

Answer: GCF of 18 and 28 is 2.

Explanation:

The GCF of two non-zero integers, x(18) and y(28), is the greatest positive integer m(2) that divides both x(18) and y(28) without any remainder.

Methods to Find GCF of 18 and 28

Let's look at the different methods for finding the GCF of 18 and 28.

Prime Factorization Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 18 and 28 by Prime Factorization

Prime factorization of 18 and 28 is (2 × 3 × 3) and (2 × 2 × 7) respectively. As visible, 18 and 28 have only one common prime factor i.e. 2. Hence, the GCF of 18 and 28 is 2.

GCF of 18 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 = 18

GCF(28, 18) = GCF(18, 28 mod 18) = GCF(18, 10)
GCF(18, 10) = GCF(10, 18 mod 10) = GCF(10, 8)
GCF(10, 8) = GCF(8, 10 mod 8) = GCF(8, 2)
GCF(8, 2) = GCF(2, 8 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 18 and 28 is 2.

GCF of 18 and 28 by Listing Common Factors

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 28: 1, 2, 4, 7, 14, 28

There are 2 common factors of 18 and 28, that are 1 and 2. Therefore, the greatest common factor of 18 and 28 is 2.

☛ Also Check:

GCF of 18 and 28 Examples

Example 1: For two numbers, GCF = 2 and LCM = 252. If one number is 28, find the other number.

Solution:

Given: GCF (y, 28) = 2 and LCM (y, 28) = 252
∵ GCF × LCM = 28 × (y)
⇒ y = (GCF × LCM)/28
⇒ y = (2 × 252)/28
⇒ y = 18
Therefore, the other number is 18.
Example 2: Find the GCF of 18 and 28, if their LCM is 252.

Solution:

∵ LCM × GCF = 18 × 28
⇒ GCF(18, 28) = (18 × 28)/252 = 2
Therefore, the greatest common factor of 18 and 28 is 2.
Example 3: Find the greatest number that divides 18 and 28 exactly.

Solution:

The greatest number that divides 18 and 28 exactly is their greatest common factor, i.e. GCF of 18 and 28.
⇒ Factors of 18 and 28:
- Factors of 18 = 1, 2, 3, 6, 9, 18
- Factors of 28 = 1, 2, 4, 7, 14, 28
Therefore, the GCF of 18 and 28 is 2.

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FAQs on GCF of 18 and 28

What is the GCF of 18 and 28?

The GCF of 18 and 28 is 2. To calculate the greatest common factor (GCF) of 18 and 28, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the greatest factor that exactly divides both 18 and 28, i.e., 2.

What are the Methods to Find GCF of 18 and 28?

There are three commonly used methods to find the GCF of 18 and 28.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the GCF of 18 and 28 by Long Division Method?

To find the GCF of 18, 28 using long division method, 28 is divided by 18. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 18, 28?

The following equation can be used to express the relation between LCM and GCF of 18 and 28, i.e. GCF × LCM = 18 × 28.

If the GCF of 28 and 18 is 2, Find its LCM.

GCF(28, 18) × LCM(28, 18) = 28 × 18
Since the GCF of 28 and 18 = 2
⇒ 2 × LCM(28, 18) = 504
Therefore, LCM = 252
☛ Greatest Common Factor Calculator

How to Find the GCF of 18 and 28 by Prime Factorization?

To find the GCF of 18 and 28, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 28 = 2 × 2 × 7.
⇒ Since 2 is the only common prime factor of 18 and 28. Hence, GCF (18, 28) = 2.
☛ Prime Number

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