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GCF of 18 and 36

GCF of 18 and 36 is the largest possible number that divides 18 and 36 exactly without any remainder. The factors of 18 and 36 are 1, 2, 3, 6, 9, 18 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There are 3 commonly used methods to find the GCF of 18 and 36 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 18 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 18 and 36?

Answer: GCF of 18 and 36 is 18.

Explanation:

The GCF of two non-zero integers, x(18) and y(36), is the greatest positive integer m(18) that divides both x(18) and y(36) without any remainder.

Methods to Find GCF of 18 and 36

Let's look at the different methods for finding the GCF of 18 and 36.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 18 and 36 by Long Division

GCF of 18 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 36 (larger number) by 18 (smaller number).
Step 2: Since the remainder = 0, the divisor (18) is the GCF of 18 and 36.

The corresponding divisor (18) is the GCF of 18 and 36.

GCF of 18 and 36 by Prime Factorization

Prime factorization of 18 and 36 is (2 × 3 × 3) and (2 × 2 × 3 × 3) respectively. As visible, 18 and 36 have common prime factors. Hence, the GCF of 18 and 36 is 2 × 3 × 3 = 18.

GCF of 18 and 36 by Listing Common Factors

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

There are 6 common factors of 18 and 36, that are 1, 2, 3, 6, 9, and 18. Therefore, the greatest common factor of 18 and 36 is 18.

☛ Also Check:

GCF of 18 and 36 Examples

Example 1: The product of two numbers is 648. If their GCF is 18, what is their LCM?

Solution:

Given: GCF = 18 and product of numbers = 648
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 648/18
Therefore, the LCM is 36.
Example 2: Find the greatest number that divides 18 and 36 exactly.

Solution:

The greatest number that divides 18 and 36 exactly is their greatest common factor, i.e. GCF of 18 and 36.
⇒ Factors of 18 and 36:
- Factors of 18 = 1, 2, 3, 6, 9, 18
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Therefore, the GCF of 18 and 36 is 18.
Example 3: For two numbers, GCF = 18 and LCM = 36. If one number is 18, find the other number.

Solution:

Given: GCF (x, 18) = 18 and LCM (x, 18) = 36
∵ GCF × LCM = 18 × (x)
⇒ x = (GCF × LCM)/18
⇒ x = (18 × 36)/18
⇒ x = 36
Therefore, the other number is 36.

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FAQs on GCF of 18 and 36

What is the GCF of 18 and 36?

The GCF of 18 and 36 is 18. To calculate the greatest common factor (GCF) of 18 and 36, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the greatest factor that exactly divides both 18 and 36, i.e., 18.

How to Find the GCF of 18 and 36 by Prime Factorization?

To find the GCF of 18 and 36, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 36 = 2 × 2 × 3 × 3.
⇒ Since 2, 3, 3 are common terms in the prime factorization of 18 and 36. Hence, GCF(18, 36) = 2 × 3 × 3 = 18
☛ Prime Number

If the GCF of 36 and 18 is 18, Find its LCM.

GCF(36, 18) × LCM(36, 18) = 36 × 18
Since the GCF of 36 and 18 = 18
⇒ 18 × LCM(36, 18) = 648
Therefore, LCM = 36
☛ Greatest Common Factor Calculator

How to Find the GCF of 18 and 36 by Long Division Method?

To find the GCF of 18, 36 using long division method, 36 is divided by 18. The corresponding divisor (18) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 18 and 36?

There are three commonly used methods to find the GCF of 18 and 36.

By Prime Factorization
By Euclidean Algorithm
By Long Division

What is the Relation Between LCM and GCF of 18, 36?

The following equation can be used to express the relation between Least Common Multiple and GCF of 18 and 36, i.e. GCF × LCM = 18 × 36.

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