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GCF of 26 and 39

GCF of 26 and 39 is the largest possible number that divides 26 and 39 exactly without any remainder. The factors of 26 and 39 are 1, 2, 13, 26 and 1, 3, 13, 39 respectively. There are 3 commonly used methods to find the GCF of 26 and 39 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 26 and 39
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 26 and 39?

Answer: GCF of 26 and 39 is 13.

Explanation:

The GCF of two non-zero integers, x(26) and y(39), is the greatest positive integer m(13) that divides both x(26) and y(39) without any remainder.

Methods to Find GCF of 26 and 39

The methods to find the GCF of 26 and 39 are explained below.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

GCF of 26 and 39 by Listing Common Factors

Factors of 26: 1, 2, 13, 26
Factors of 39: 1, 3, 13, 39

There are 2 common factors of 26 and 39, that are 1 and 13. Therefore, the greatest common factor of 26 and 39 is 13.

GCF of 26 and 39 by Prime Factorization

Prime factorization of 26 and 39 is (2 × 13) and (3 × 13) respectively. As visible, 26 and 39 have only one common prime factor i.e. 13. Hence, the GCF of 26 and 39 is 13.

GCF of 26 and 39 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 = 39 and Y = 26

GCF(39, 26) = GCF(26, 39 mod 26) = GCF(26, 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 26 and 39 is 13.

☛ Also Check:

GCF of 26 and 39 Examples

Example 1: For two numbers, GCF = 13 and LCM = 78. If one number is 26, find the other number.

Solution:

Given: GCF (x, 26) = 13 and LCM (x, 26) = 78
∵ GCF × LCM = 26 × (x)
⇒ x = (GCF × LCM)/26
⇒ x = (13 × 78)/26
⇒ x = 39
Therefore, the other number is 39.
Example 2: Find the greatest number that divides 26 and 39 exactly.

Solution:

The greatest number that divides 26 and 39 exactly is their greatest common factor, i.e. GCF of 26 and 39.
⇒ Factors of 26 and 39:
- Factors of 26 = 1, 2, 13, 26
- Factors of 39 = 1, 3, 13, 39
Therefore, the GCF of 26 and 39 is 13.
Example 3: Find the GCF of 26 and 39, if their LCM is 78.

Solution:

∵ LCM × GCF = 26 × 39
⇒ GCF(26, 39) = (26 × 39)/78 = 13
Therefore, the greatest common factor of 26 and 39 is 13.

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FAQs on GCF of 26 and 39

What is the GCF of 26 and 39?

The GCF of 26 and 39 is 13. To calculate the greatest common factor of 26 and 39, we need to factor each number (factors of 26 = 1, 2, 13, 26; factors of 39 = 1, 3, 13, 39) and choose the greatest factor that exactly divides both 26 and 39, i.e., 13.

If the GCF of 39 and 26 is 13, Find its LCM.

GCF(39, 26) × LCM(39, 26) = 39 × 26
Since the GCF of 39 and 26 = 13
⇒ 13 × LCM(39, 26) = 1014
Therefore, LCM = 78
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How to Find the GCF of 26 and 39 by Prime Factorization?

To find the GCF of 26 and 39, we will find the prime factorization of the given numbers, i.e. 26 = 2 × 13; 39 = 3 × 13.
⇒ Since 13 is the only common prime factor of 26 and 39. Hence, GCF (26, 39) = 13.
☛ Prime Numbers

How to Find the GCF of 26 and 39 by Long Division Method?

To find the GCF of 26, 39 using long division method, 39 is divided by 26. The corresponding divisor (13) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 26, 39?

The following equation can be used to express the relation between Least Common Multiple and GCF of 26 and 39, i.e. GCF × LCM = 26 × 39.

What are the Methods to Find GCF of 26 and 39?

There are three commonly used methods to find the GCF of 26 and 39.

By Long Division
By Listing Common Factors
By Prime Factorization

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