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GCF of 9 and 18

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

1.	GCF of 9 and 18
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 9 and 18?

Answer: GCF of 9 and 18 is 9.

Explanation:

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

Methods to Find GCF of 9 and 18

Let's look at the different methods for finding the GCF of 9 and 18.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 9 and 18 by Listing Common Factors

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

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

GCF of 9 and 18 by Prime Factorization

Prime factorization of 9 and 18 is (3 × 3) and (2 × 3 × 3) respectively. As visible, 9 and 18 have common prime factors. Hence, the GCF of 9 and 18 is 3 × 3 = 9.

GCF of 9 and 18 by Long Division

GCF of 9 and 18 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 18 (larger number) by 9 (smaller number).
Step 2: Since the remainder = 0, the divisor (9) is the GCF of 9 and 18.

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

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GCF of 9 and 18 Examples

Example 1: The product of two numbers is 162. If their GCF is 9, what is their LCM?

Solution:

Given: GCF = 9 and product of numbers = 162
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 162/9
Therefore, the LCM is 18.
Example 2: Find the GCF of 9 and 18, if their LCM is 18.

Solution:

∵ LCM × GCF = 9 × 18
⇒ GCF(9, 18) = (9 × 18)/18 = 9
Therefore, the greatest common factor of 9 and 18 is 9.
Example 3: For two numbers, GCF = 9 and LCM = 18. If one number is 9, find the other number.

Solution:

Given: GCF (x, 9) = 9 and LCM (x, 9) = 18
∵ GCF × LCM = 9 × (x)
⇒ x = (GCF × LCM)/9
⇒ x = (9 × 18)/9
⇒ x = 18
Therefore, the other number is 18.

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FAQs on GCF of 9 and 18

What is the GCF of 9 and 18?

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

How to Find the GCF of 9 and 18 by Prime Factorization?

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

What is the Relation Between LCM and GCF of 9, 18?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 9 and 18, i.e. GCF × LCM = 9 × 18.

What are the Methods to Find GCF of 9 and 18?

There are three commonly used methods to find the GCF of 9 and 18.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the GCF of 9 and 18 by Long Division Method?

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

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

GCF(18, 9) × LCM(18, 9) = 18 × 9
Since the GCF of 18 and 9 = 9
⇒ 9 × LCM(18, 9) = 162
Therefore, LCM = 18
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