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GCF of 9 and 11

GCF of 9 and 11 is the largest possible number that divides 9 and 11 exactly without any remainder. The factors of 9 and 11 are 1, 3, 9 and 1, 11 respectively. There are 3 commonly used methods to find the GCF of 9 and 11 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 9 and 11
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 9 and 11?

Answer: GCF of 9 and 11 is 1.

Explanation:

The GCF of two non-zero integers, x(9) and y(11), is the greatest positive integer m(1) that divides both x(9) and y(11) without any remainder.

Methods to Find GCF of 9 and 11

Let's look at the different methods for finding the GCF of 9 and 11.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 9 and 11 by Prime Factorization

Prime factorization of 9 and 11 is (3 × 3) and (11) respectively. As visible, there are no common prime factors between 9 and 11, i.e. they are co-prime. Hence, the GCF of 9 and 11 will be 1.

GCF of 9 and 11 by Long Division

GCF of 9 and 11 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 11 (larger number) by 9 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (9) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 9 and 11.

GCF of 9 and 11 by Listing Common Factors

Factors of 9: 1, 3, 9
Factors of 11: 1, 11

Since, 1 is the only common factor between 9 and 11. The Greatest Common Factor of 9 and 11 is 1.

☛ Also Check:

GCF of 9 and 11 Examples

Example 1: For two numbers, GCF = 1 and LCM = 99. If one number is 9, find the other number.

Solution:

Given: GCF (x, 9) = 1 and LCM (x, 9) = 99
∵ GCF × LCM = 9 × (x)
⇒ x = (GCF × LCM)/9
⇒ x = (1 × 99)/9
⇒ x = 11
Therefore, the other number is 11.
Example 2: The product of two numbers is 99. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 99
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 99/1
Therefore, the LCM is 99.
Example 3: Find the GCF of 9 and 11, if their LCM is 99.

Solution:

∵ LCM × GCF = 9 × 11
⇒ GCF(9, 11) = (9 × 11)/99 = 1
Therefore, the greatest common factor of 9 and 11 is 1.

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FAQs on GCF of 9 and 11

What is the GCF of 9 and 11?

The GCF of 9 and 11 is 1. To calculate the greatest common factor (GCF) of 9 and 11, we need to factor each number (factors of 9 = 1, 3, 9; factors of 11 = 1, 11) and choose the greatest factor that exactly divides both 9 and 11, i.e., 1.

How to Find the GCF of 9 and 11 by Prime Factorization?

To find the GCF of 9 and 11, we will find the prime factorization of the given numbers, i.e. 9 = 3 × 3; 11 = 11.
⇒ There is no common prime factor for 9 and 11. Hence, GCF (9, 11) = 1.
☛ Prime Number

What is the Relation Between LCM and GCF of 9, 11?

The following equation can be used to express the relation between LCM and GCF of 9 and 11, i.e. GCF × LCM = 9 × 11.

What are the Methods to Find GCF of 9 and 11?

There are three commonly used methods to find the GCF of 9 and 11.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 9 and 11 by Long Division Method?

To find the GCF of 9, 11 using long division method, 11 is divided by 9. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

If the GCF of 11 and 9 is 1, Find its LCM.

GCF(11, 9) × LCM(11, 9) = 11 × 9
Since the GCF of 11 and 9 = 1
⇒ 1 × LCM(11, 9) = 99
Therefore, LCM = 99
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