GCF that 26 and also 39 is the largest feasible number that divides 26 and 39 specifically without any remainder. The components of 26 and also 39 are 1, 2, 13, 26 and 1, 3, 13, 39 respectively. There room 3 generally used approaches to discover the GCF of 26 and also 39 - prime factorization, Euclidean algorithm, and long division.

You are watching: Greatest common factor of 26 and 39

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

Answer: GCF of 26 and also 39 is 13.

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Explanation:

The GCF of 2 non-zero integers, x(26) and also y(39), is the biggest positive integer m(13) that divides both x(26) and also y(39) without any remainder.


The methods to uncover the GCF the 26 and also 39 are explained below.

Listing typical FactorsPrime factorization MethodUsing Euclid's Algorithm

GCF that 26 and also 39 by Listing common Factors

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

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

GCF that 26 and also 39 by prime Factorization

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

GCF that 26 and 39 through Euclidean Algorithm

As every the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mode 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 mod 13) = GCF(13, 0)GCF(13, 0) = 13 (∵ GCF(X, 0) = |X|, where X ≠ 0)

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

☛ also Check:


GCF that 26 and also 39 Examples


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

Solution:

Given: GCF (x, 26) = 13 and also LCM (x, 26) = 78∵ GCF × LCM = 26 × (x)⇒ x = (GCF × LCM)/26⇒ x = (13 × 78)/26⇒ x = 39Therefore, the other number is 39.


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

Solution:

The greatest number the divides 26 and also 39 exactly is their greatest usual factor, i.e. GCF that 26 and 39.⇒ factors of 26 and 39:

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

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


Example 3: uncover the GCF that 26 and also 39, if your LCM is 78.

Solution:

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


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FAQs top top GCF of 26 and 39

What is the GCF that 26 and also 39?

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

If the GCF that 39 and also 26 is 13, discover 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 find the GCF the 26 and 39 by element Factorization?

To uncover the GCF of 26 and also 39, us will find the prime factorization the the given numbers, i.e. 26 = 2 × 13; 39 = 3 × 13.⇒ because 13 is the only typical prime aspect of 26 and also 39. Hence, GCF (26, 39) = 13.☛ prime Numbers

How to find the GCF of 26 and 39 through Long department Method?

To find the GCF of 26, 39 using long department method, 39 is separated by 26. The equivalent divisor (13) once remainder amounts to 0 is taken as GCF.

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

The adhering to equation have the right to be supplied to to express the relation between Least common Multiple and also GCF that 26 and 39, i.e. GCF × LCM = 26 × 39.

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What room the methods to uncover GCF of 26 and also 39?

There space three typically used techniques to discover the GCF of 26 and 39.