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GCF of 18 and 63

GCF of 18 and 63 is the largest possible number that divides 18 and 63 exactly without any remainder. The factors of 18 and 63 are 1, 2, 3, 6, 9, 18 and 1, 3, 7, 9, 21, 63 respectively. There are 3 commonly used methods to find the GCF of 18 and 63 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 18 and 63
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 18 and 63?

Answer: GCF of 18 and 63 is 9.

Explanation:

The GCF of two non-zero integers, x(18) and y(63), is the greatest positive integer m(9) that divides both x(18) and y(63) without any remainder.

Methods to Find GCF of 18 and 63

The methods to find the GCF of 18 and 63 are explained below.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 18 and 63 by Long Division

GCF of 18 and 63 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 63 (larger number) by 18 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (9).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (9) is the GCF of 18 and 63.

GCF of 18 and 63 by Listing Common Factors

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 63: 1, 3, 7, 9, 21, 63

There are 3 common factors of 18 and 63, that are 1, 3, and 9. Therefore, the greatest common factor of 18 and 63 is 9.

GCF of 18 and 63 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 = 63 and Y = 18

GCF(63, 18) = GCF(18, 63 mod 18) = GCF(18, 9)
GCF(18, 9) = GCF(9, 18 mod 9) = GCF(9, 0)
GCF(9, 0) = 9 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 18 and 63 is 9.

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GCF of 18 and 63 Examples

Example 1: For two numbers, GCF = 9 and LCM = 126. If one number is 18, find the other number.

Solution:

Given: GCF (x, 18) = 9 and LCM (x, 18) = 126
∵ GCF × LCM = 18 × (x)
⇒ x = (GCF × LCM)/18
⇒ x = (9 × 126)/18
⇒ x = 63
Therefore, the other number is 63.
Example 2: Find the GCF of 18 and 63, if their LCM is 126.

Solution:

∵ LCM × GCF = 18 × 63
⇒ GCF(18, 63) = (18 × 63)/126 = 9
Therefore, the greatest common factor of 18 and 63 is 9.
Example 3: The product of two numbers is 1134. If their GCF is 9, what is their LCM?

Solution:

Given: GCF = 9 and product of numbers = 1134
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1134/9
Therefore, the LCM is 126.

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FAQs on GCF of 18 and 63

What is the GCF of 18 and 63?

The GCF of 18 and 63 is 9. To calculate the GCF (Greatest Common Factor) of 18 and 63, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the greatest factor that exactly divides both 18 and 63, i.e., 9.

What are the Methods to Find GCF of 18 and 63?

There are three commonly used methods to find the GCF of 18 and 63.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 18 and 63 by Long Division Method?

To find the GCF of 18, 63 using long division method, 63 is divided by 18. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 18, 63?

The following equation can be used to express the relation between LCM and GCF of 18 and 63, i.e. GCF × LCM = 18 × 63.

If the GCF of 63 and 18 is 9, Find its LCM.

GCF(63, 18) × LCM(63, 18) = 63 × 18
Since the GCF of 63 and 18 = 9
⇒ 9 × LCM(63, 18) = 1134
Therefore, LCM = 126
☛ Greatest Common Factor Calculator

How to Find the GCF of 18 and 63 by Prime Factorization?

To find the GCF of 18 and 63, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 63 = 3 × 3 × 7.
⇒ Since 3, 3 are common terms in the prime factorization of 18 and 63. Hence, GCF(18, 63) = 3 × 3 = 9
☛ What are Prime Numbers?

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