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GCF of 11 and 13

GCF of 11 and 13 is the largest possible number that divides 11 and 13 exactly without any remainder. The factors of 11 and 13 are 1, 11 and 1, 13 respectively. There are 3 commonly used methods to find the GCF of 11 and 13 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 11 and 13
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 11 and 13?

Answer: GCF of 11 and 13 is 1.

Explanation:

The GCF of two non-zero integers, x(11) and y(13), is the greatest positive integer m(1) that divides both x(11) and y(13) without any remainder.

Methods to Find GCF of 11 and 13

The methods to find the GCF of 11 and 13 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 11 and 13 by Long Division

GCF of 11 and 13 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 13 (larger number) by 11 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (11) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 11 and 13.

GCF of 11 and 13 by Prime Factorization

Prime factorization of 11 and 13 is (11) and (13) respectively. As visible, there are no common prime factors between 11 and 13, i.e. they are co-prime. Hence, the GCF of 11 and 13 will be 1.

GCF of 11 and 13 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 = 13 and Y = 11

GCF(13, 11) = GCF(11, 13 mod 11) = GCF(11, 2)
GCF(11, 2) = GCF(2, 11 mod 2) = GCF(2, 1)
GCF(2, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 11 and 13 is 1.

☛ Also Check:

GCF of 11 and 13 Examples

Example 1: Find the greatest number that divides 11 and 13 exactly.

Solution:

The greatest number that divides 11 and 13 exactly is their greatest common factor, i.e. GCF of 11 and 13.
⇒ Factors of 11 and 13:
- Factors of 11 = 1, 11
- Factors of 13 = 1, 13
Therefore, the GCF of 11 and 13 is 1.
Example 2: For two numbers, GCF = 1 and LCM = 143. If one number is 13, find the other number.

Solution:

Given: GCF (x, 13) = 1 and LCM (x, 13) = 143
∵ GCF × LCM = 13 × (x)
⇒ x = (GCF × LCM)/13
⇒ x = (1 × 143)/13
⇒ x = 11
Therefore, the other number is 11.
Example 3: Find the GCF of 11 and 13, if their LCM is 143.

Solution:

∵ LCM × GCF = 11 × 13
⇒ GCF(11, 13) = (11 × 13)/143 = 1
Therefore, the greatest common factor of 11 and 13 is 1.

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FAQs on GCF of 11 and 13

What is the GCF of 11 and 13?

The GCF of 11 and 13 is 1. To calculate the greatest common factor (GCF) of 11 and 13, we need to factor each number (factors of 11 = 1, 11; factors of 13 = 1, 13) and choose the greatest factor that exactly divides both 11 and 13, i.e., 1.

What is the Relation Between LCM and GCF of 11, 13?

The following equation can be used to express the relation between Least Common Multiple and GCF of 11 and 13, i.e. GCF × LCM = 11 × 13.

How to Find the GCF of 11 and 13 by Prime Factorization?

To find the GCF of 11 and 13, we will find the prime factorization of the given numbers, i.e. 11 = 11; 13 = 13.
⇒ There is no common prime factor for 11 and 13. Hence, GCF (11, 13) = 1.
☛ What is a Prime Number?

What are the Methods to Find GCF of 11 and 13?

There are three commonly used methods to find the GCF of 11 and 13.

By Long Division
By Euclidean Algorithm
By Prime Factorization

If the GCF of 13 and 11 is 1, Find its LCM.

GCF(13, 11) × LCM(13, 11) = 13 × 11
Since the GCF of 13 and 11 = 1
⇒ 1 × LCM(13, 11) = 143
Therefore, LCM = 143
☛ Greatest Common Factor Calculator

How to Find the GCF of 11 and 13 by Long Division Method?

To find the GCF of 11, 13 using long division method, 13 is divided by 11. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

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