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GCF of 18 and 30

GCF of 18 and 30 is the largest possible number that divides 18 and 30 exactly without any remainder. The factors of 18 and 30 are 1, 2, 3, 6, 9, 18 and 1, 2, 3, 5, 6, 10, 15, 30 respectively. There are 3 commonly used methods to find the GCF of 18 and 30 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 18 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 18 and 30?

Answer: GCF of 18 and 30 is 6.

Explanation:

The GCF of two non-zero integers, x(18) and y(30), is the greatest positive integer m(6) that divides both x(18) and y(30) without any remainder.

Methods to Find GCF of 18 and 30

Let's look at the different methods for finding the GCF of 18 and 30.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 18 and 30 by Long Division

GCF of 18 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 18 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the GCF of 18 and 30.

GCF of 18 and 30 by Listing Common Factors

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

There are 4 common factors of 18 and 30, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 18 and 30 is 6.

GCF of 18 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 = 18

GCF(30, 18) = GCF(18, 30 mod 18) = GCF(18, 12)
GCF(18, 12) = GCF(12, 18 mod 12) = GCF(12, 6)
GCF(12, 6) = GCF(6, 12 mod 6) = GCF(6, 0)
GCF(6, 0) = 6 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 18 and 30 is 6.

☛ Also Check:

GCF of 18 and 30 Examples

Example 1: Find the GCF of 18 and 30, if their LCM is 90.

Solution:

∵ LCM × GCF = 18 × 30
⇒ GCF(18, 30) = (18 × 30)/90 = 6
Therefore, the greatest common factor of 18 and 30 is 6.
Example 2: For two numbers, GCF = 6 and LCM = 90. If one number is 30, find the other number.

Solution:

Given: GCF (x, 30) = 6 and LCM (x, 30) = 90
∵ GCF × LCM = 30 × (x)
⇒ x = (GCF × LCM)/30
⇒ x = (6 × 90)/30
⇒ x = 18
Therefore, the other number is 18.
Example 3: The product of two numbers is 540. If their GCF is 6, what is their LCM?

Solution:

Given: GCF = 6 and product of numbers = 540
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 540/6
Therefore, the LCM is 90.

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FAQs on GCF of 18 and 30

What is the GCF of 18 and 30?

The GCF of 18 and 30 is 6. To calculate the greatest common factor (GCF) of 18 and 30, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the greatest factor that exactly divides both 18 and 30, i.e., 6.

What is the Relation Between LCM and GCF of 18, 30?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 18 and 30, i.e. GCF × LCM = 18 × 30.

What are the Methods to Find GCF of 18 and 30?

There are three commonly used methods to find the GCF of 18 and 30.

By Listing Common Factors
By Long Division
By Prime Factorization

If the GCF of 30 and 18 is 6, Find its LCM.

GCF(30, 18) × LCM(30, 18) = 30 × 18
Since the GCF of 30 and 18 = 6
⇒ 6 × LCM(30, 18) = 540
Therefore, LCM = 90
☛ Greatest Common Factor Calculator

How to Find the GCF of 18 and 30 by Long Division Method?

To find the GCF of 18, 30 using long division method, 30 is divided by 18. The corresponding divisor (6) when remainder equals 0 is taken as GCF.

How to Find the GCF of 18 and 30 by Prime Factorization?

To find the GCF of 18 and 30, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 30 = 2 × 3 × 5.
⇒ Since 2, 3 are common terms in the prime factorization of 18 and 30. Hence, GCF(18, 30) = 2 × 3 = 6
☛ Prime Number

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