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GCF of 11 and 15

GCF of 11 and 15 is the largest possible number that divides 11 and 15 exactly without any remainder. The factors of 11 and 15 are 1, 11 and 1, 3, 5, 15 respectively. There are 3 commonly used methods to find the GCF of 11 and 15 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 11 and 15
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 11 and 15?

Answer: GCF of 11 and 15 is 1.

Explanation:

The GCF of two non-zero integers, x(11) and y(15), is the greatest positive integer m(1) that divides both x(11) and y(15) without any remainder.

Methods to Find GCF of 11 and 15

The methods to find the GCF of 11 and 15 are explained below.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

GCF of 11 and 15 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 = 15 and Y = 11

GCF(15, 11) = GCF(11, 15 mod 11) = GCF(11, 4)
GCF(11, 4) = GCF(4, 11 mod 4) = GCF(4, 3)
GCF(4, 3) = GCF(3, 4 mod 3) = GCF(3, 1)
GCF(3, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 11 and 15 is 1.

GCF of 11 and 15 by Listing Common Factors

Factors of 11: 1, 11
Factors of 15: 1, 3, 5, 15

Since, 1 is the only common factor between 11 and 15. The Greatest Common Factor of 11 and 15 is 1.

GCF of 11 and 15 by Long Division

GCF of 11 and 15 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 15 (larger number) by 11 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (11) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 11 and 15.

☛ Also Check:

GCF of 11 and 15 Examples

Example 1: Find the GCF of 11 and 15, if their LCM is 165.

Solution:

∵ LCM × GCF = 11 × 15
⇒ GCF(11, 15) = (11 × 15)/165 = 1
Therefore, the greatest common factor of 11 and 15 is 1.
Example 2: The product of two numbers is 165. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 165
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 165/1
Therefore, the LCM is 165.
Example 3: Find the greatest number that divides 11 and 15 exactly.

Solution:

The greatest number that divides 11 and 15 exactly is their greatest common factor, i.e. GCF of 11 and 15.
⇒ Factors of 11 and 15:
- Factors of 11 = 1, 11
- Factors of 15 = 1, 3, 5, 15
Therefore, the GCF of 11 and 15 is 1.

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FAQs on GCF of 11 and 15

What is the GCF of 11 and 15?

The GCF of 11 and 15 is 1. To calculate the greatest common factor of 11 and 15, we need to factor each number (factors of 11 = 1, 11; factors of 15 = 1, 3, 5, 15) and choose the greatest factor that exactly divides both 11 and 15, i.e., 1.

How to Find the GCF of 11 and 15 by Prime Factorization?

To find the GCF of 11 and 15, we will find the prime factorization of the given numbers, i.e. 11 = 11; 15 = 3 × 5.
⇒ There is no common prime factor for 11 and 15. Hence, GCF (11, 15) = 1.
☛ Prime Number

What is the Relation Between LCM and GCF of 11, 15?

The following equation can be used to express the relation between Least Common Multiple and GCF of 11 and 15, i.e. GCF × LCM = 11 × 15.

How to Find the GCF of 11 and 15 by Long Division Method?

To find the GCF of 11, 15 using long division method, 15 is divided by 11. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 11 and 15?

There are three commonly used methods to find the GCF of 11 and 15.

By Listing Common Factors
By Long Division
By Prime Factorization

If the GCF of 15 and 11 is 1, Find its LCM.

GCF(15, 11) × LCM(15, 11) = 15 × 11
Since the GCF of 15 and 11 = 1
⇒ 1 × LCM(15, 11) = 165
Therefore, LCM = 165
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