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GCF of 18 and 21

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

1.	GCF of 18 and 21
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 18 and 21?

Answer: GCF of 18 and 21 is 3.

Explanation:

The GCF of two non-zero integers, x(18) and y(21), is the greatest positive integer m(3) that divides both x(18) and y(21) without any remainder.

Methods to Find GCF of 18 and 21

The methods to find the GCF of 18 and 21 are explained below.

Listing Common Factors
Using Euclid's Algorithm
Prime Factorization Method

GCF of 18 and 21 by Listing Common Factors

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

There are 2 common factors of 18 and 21, that are 1 and 3. Therefore, the greatest common factor of 18 and 21 is 3.

GCF of 18 and 21 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 = 21 and Y = 18

GCF(21, 18) = GCF(18, 21 mod 18) = GCF(18, 3)
GCF(18, 3) = GCF(3, 18 mod 3) = GCF(3, 0)
GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 18 and 21 is 3.

GCF of 18 and 21 by Prime Factorization

Prime factorization of 18 and 21 is (2 × 3 × 3) and (3 × 7) respectively. As visible, 18 and 21 have only one common prime factor i.e. 3. Hence, the GCF of 18 and 21 is 3.

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GCF of 18 and 21 Examples

Example 1: Find the greatest number that divides 18 and 21 exactly.

Solution:

The greatest number that divides 18 and 21 exactly is their greatest common factor, i.e. GCF of 18 and 21.
⇒ Factors of 18 and 21:
- Factors of 18 = 1, 2, 3, 6, 9, 18
- Factors of 21 = 1, 3, 7, 21
Therefore, the GCF of 18 and 21 is 3.
Example 2: For two numbers, GCF = 3 and LCM = 126. If one number is 21, find the other number.

Solution:

Given: GCF (z, 21) = 3 and LCM (z, 21) = 126
∵ GCF × LCM = 21 × (z)
⇒ z = (GCF × LCM)/21
⇒ z = (3 × 126)/21
⇒ z = 18
Therefore, the other number is 18.
Example 3: The product of two numbers is 378. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 378
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 378/3
Therefore, the LCM is 126.

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FAQs on GCF of 18 and 21

What is the GCF of 18 and 21?

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

What is the Relation Between LCM and GCF of 18, 21?

The following equation can be used to express the relation between Least Common Multiple and GCF of 18 and 21, i.e. GCF × LCM = 18 × 21.

How to Find the GCF of 18 and 21 by Long Division Method?

To find the GCF of 18, 21 using long division method, 21 is divided by 18. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 18 and 21?

There are three commonly used methods to find the GCF of 18 and 21.

By Long Division
By Prime Factorization
By Listing Common Factors

If the GCF of 21 and 18 is 3, Find its LCM.

GCF(21, 18) × LCM(21, 18) = 21 × 18
Since the GCF of 21 and 18 = 3
⇒ 3 × LCM(21, 18) = 378
Therefore, LCM = 126
☛ Greatest Common Factor Calculator

How to Find the GCF of 18 and 21 by Prime Factorization?

To find the GCF of 18 and 21, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 21 = 3 × 7.
⇒ Since 3 is the only common prime factor of 18 and 21. Hence, GCF (18, 21) = 3.
☛ Prime Number

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