GCF the 26 and 39 is the largest possible number that divides 26 and also 39 precisely without any type of remainder. The components of 26 and 39 space 1, 2, 13, 26 and also 1, 3, 13, 39 respectively. There space 3 typically used techniques to discover the GCF that 26 and 39 - element factorization, Euclidean algorithm, and also long division.

You are watching: Greatest common factor of 26 and 39

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

Answer: GCF the 26 and 39 is 13.

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Explanation:

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


The approaches to discover the GCF the 26 and also 39 are explained below.

Listing usual FactorsPrime factorization MethodUsing Euclid's Algorithm

GCF the 26 and also 39 through Listing common Factors

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Factors that 26: 1, 2, 13, 26Factors the 39: 1, 3, 13, 39

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

GCF that 26 and 39 by prime Factorization

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

GCF of 26 and 39 by Euclidean Algorithm

As every the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)where X > Y and also mod is the modulo operator.

Here X = 39 and also Y = 26

GCF(39, 26) = GCF(26, 39 mod 26) = GCF(26, 13)GCF(26, 13) = GCF(13, 26 mode 13) = GCF(13, 0)GCF(13, 0) = 13 (∵ GCF(X, 0) = |X|, wherein X ≠ 0)

Therefore, the value of GCF of 26 and also 39 is 13.

☛ also Check:


GCF the 26 and 39 Examples


Example 1: For two numbers, GCF = 13 and also LCM = 78. If one number is 26, find the various 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 = 39Therefore, the various other number is 39.


Example 2: find the best number the divides 26 and also 39 exactly.

Solution:

The greatest number the divides 26 and 39 precisely is their greatest common factor, i.e. GCF the 26 and also 39.⇒ components of 26 and 39:

Factors the 26 = 1, 2, 13, 26Factors of 39 = 1, 3, 13, 39

Therefore, the GCF that 26 and 39 is 13.


Example 3: discover the GCF of 26 and also 39, if their LCM is 78.

Solution:

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


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FAQs ~ above GCF that 26 and 39

What is the GCF of 26 and 39?

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

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

GCF(39, 26) × LCM(39, 26) = 39 × 26Since the GCF of 39 and 26 = 13⇒ 13 × LCM(39, 26) = 1014Therefore, LCM = 78☛ GCF Calculator

How to discover the GCF that 26 and 39 by element Factorization?

To discover the GCF of 26 and also 39, we will find the prime factorization that the provided numbers, i.e. 26 = 2 × 13; 39 = 3 × 13.⇒ due to the fact that 13 is the only usual prime factor of 26 and also 39. Hence, GCF (26, 39) = 13.☛ prime Numbers

How to discover the GCF that 26 and 39 by Long department Method?

To discover the GCF the 26, 39 using long division method, 39 is separated by 26. The corresponding divisor (13) when remainder equates to 0 is taken as GCF.

What is the Relation in between LCM and also GCF that 26, 39?

The following equation have the right to be provided to refer the relation in between Least usual Multiple and GCF that 26 and 39, i.e. GCF × LCM = 26 × 39.

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What room the approaches to uncover GCF that 26 and also 39?

There are three typically used methods to discover the GCF the 26 and also 39.