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GCF of 13 and 26

GCF of 13 and 26 is the largest possible number that divides 13 and 26 exactly without any remainder. The factors of 13 and 26 are 1, 13 and 1, 2, 13, 26 respectively. There are 3 commonly used methods to find the GCF of 13 and 26 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 13 and 26
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 13 and 26?

Answer: GCF of 13 and 26 is 13.

Explanation:

The GCF of two non-zero integers, x(13) and y(26), is the greatest positive integer m(13) that divides both x(13) and y(26) without any remainder.

Methods to Find GCF of 13 and 26

The methods to find the GCF of 13 and 26 are explained below.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

GCF of 13 and 26 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 = 26 and Y = 13

GCF(26, 13) = GCF(13, 26 mod 13) = GCF(13, 0)
GCF(13, 0) = 13 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 13 and 26 is 13.

GCF of 13 and 26 by Prime Factorization

Prime factorization of 13 and 26 is (13) and (2 × 13) respectively. As visible, 13 and 26 have only one common prime factor i.e. 13. Hence, the GCF of 13 and 26 is 13.

GCF of 13 and 26 by Long Division

GCF of 13 and 26 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 26 (larger number) by 13 (smaller number).
Step 2: Since the remainder = 0, the divisor (13) is the GCF of 13 and 26.

The corresponding divisor (13) is the GCF of 13 and 26.

☛ Also Check:

GCF of 13 and 26 Examples

Example 1: Find the GCF of 13 and 26, if their LCM is 26.

Solution:

∵ LCM × GCF = 13 × 26
⇒ GCF(13, 26) = (13 × 26)/26 = 13
Therefore, the greatest common factor of 13 and 26 is 13.
Example 2: The product of two numbers is 338. If their GCF is 13, what is their LCM?

Solution:

Given: GCF = 13 and product of numbers = 338
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 338/13
Therefore, the LCM is 26.
Example 3: Find the greatest number that divides 13 and 26 exactly.

Solution:

The greatest number that divides 13 and 26 exactly is their greatest common factor, i.e. GCF of 13 and 26.
⇒ Factors of 13 and 26:
- Factors of 13 = 1, 13
- Factors of 26 = 1, 2, 13, 26
Therefore, the GCF of 13 and 26 is 13.

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FAQs on GCF of 13 and 26

What is the GCF of 13 and 26?

The GCF of 13 and 26 is 13. To calculate the GCF (Greatest Common Factor) of 13 and 26, we need to factor each number (factors of 13 = 1, 13; factors of 26 = 1, 2, 13, 26) and choose the greatest factor that exactly divides both 13 and 26, i.e., 13.

How to Find the GCF of 13 and 26 by Long Division Method?

To find the GCF of 13, 26 using long division method, 26 is divided by 13. The corresponding divisor (13) when remainder equals 0 is taken as GCF.

How to Find the GCF of 13 and 26 by Prime Factorization?

To find the GCF of 13 and 26, we will find the prime factorization of the given numbers, i.e. 13 = 13; 26 = 2 × 13.
⇒ Since 13 is the only common prime factor of 13 and 26. Hence, GCF (13, 26) = 13.
☛ Prime Numbers

If the GCF of 26 and 13 is 13, Find its LCM.

GCF(26, 13) × LCM(26, 13) = 26 × 13
Since the GCF of 26 and 13 = 13
⇒ 13 × LCM(26, 13) = 338
Therefore, LCM = 26
☛ GCF Calculator

What are the Methods to Find GCF of 13 and 26?

There are three commonly used methods to find the GCF of 13 and 26.

By Listing Common Factors
By Prime Factorization
By Long Division

What is the Relation Between LCM and GCF of 13, 26?

The following equation can be used to express the relation between LCM and GCF of 13 and 26, i.e. GCF × LCM = 13 × 26.

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