GCF that 26 and also 52 is the largest possible number that divides 26 and 52 exactly without any remainder. The components of 26 and 52 space 1, 2, 13, 26 and 1, 2, 4, 13, 26, 52 respectively. There are 3 generally used approaches to uncover the GCF of 26 and also 52 - long division, prime factorization, and Euclidean algorithm.

You are watching: What is the greatest common factor of 52 and 26

1.GCF the 26 and 52
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF that 26 and 52 is 26.

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Explanation:

The GCF of 2 non-zero integers, x(26) and y(52), is the greatest positive integer m(26) the divides both x(26) and y(52) without any type of remainder.


The approaches to discover the GCF of 26 and 52 are described below.

Using Euclid's AlgorithmListing common FactorsLong division Method

GCF of 26 and also 52 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 = 52 and Y = 26

GCF(52, 26) = GCF(26, 52 mod 26) = GCF(26, 0)GCF(26, 0) = 26 (∵ GCF(X, 0) = |X|, wherein X ≠ 0)

Therefore, the value of GCF of 26 and 52 is 26.

GCF the 26 and also 52 through Listing typical Factors

Factors of 26: 1, 2, 13, 26Factors that 52: 1, 2, 4, 13, 26, 52

There are 4 typical factors of 26 and 52, that space 1, 2, 26, and also 13. Therefore, the greatest typical factor of 26 and 52 is 26.

GCF of 26 and 52 by lengthy Division

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GCF the 26 and also 52 is the divisor that we obtain when the remainder i do not care 0 after doing long division repeatedly.

Step 2: due to the fact that the remainder = 0, the divisor (26) is the GCF that 26 and 52.

The matching divisor (26) is the GCF that 26 and also 52.

☛ additionally Check:


GCF of 26 and also 52 Examples


Example 1: The product of 2 numbers is 1352. If their GCF is 26, what is their LCM?

Solution:

Given: GCF = 26 and product of number = 1352∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 1352/26Therefore, the LCM is 52.


Example 2: find the GCF of 26 and also 52, if their LCM is 52.

Solution:

∵ LCM × GCF = 26 × 52⇒ GCF(26, 52) = (26 × 52)/52 = 26Therefore, the greatest common factor the 26 and 52 is 26.


Example 3: For two numbers, GCF = 26 and LCM = 52. If one number is 26, uncover the other number.

Solution:

Given: GCF (x, 26) = 26 and LCM (x, 26) = 52∵ GCF × LCM = 26 × (x)⇒ x = (GCF × LCM)/26⇒ x = (26 × 52)/26⇒ x = 52Therefore, the other number is 52.


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FAQs on GCF the 26 and also 52

What is the GCF of 26 and 52?

The GCF the 26 and 52 is 26. To calculation the GCF (Greatest common Factor) of 26 and also 52, we require to element each number (factors that 26 = 1, 2, 13, 26; factors of 52 = 1, 2, 4, 13, 26, 52) and also choose the greatest element that specifically divides both 26 and also 52, i.e., 26.

How to discover the GCF that 26 and also 52 by element Factorization?

To find the GCF of 26 and also 52, we will uncover the prime factorization that the offered numbers, i.e. 26 = 2 × 13; 52 = 2 × 2 × 13.⇒ due to the fact that 2, 13 are common terms in the prime factorization of 26 and also 52. Hence, GCF(26, 52) = 2 × 13 = 26☛ prime Number

How to uncover the GCF the 26 and also 52 through Long division Method?

To uncover the GCF of 26, 52 using long department method, 52 is separated by 26. The equivalent divisor (26) as soon as remainder equals 0 is taken together GCF.

If the GCF that 52 and 26 is 26, uncover its LCM.

GCF(52, 26) × LCM(52, 26) = 52 × 26Since the GCF of 52 and 26 = 26⇒ 26 × LCM(52, 26) = 1352Therefore, LCM = 52☛ Greatest typical Factor Calculator

What space the methods to uncover GCF that 26 and also 52?

There room three generally used techniques to uncover the GCF of 26 and also 52.

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By element FactorizationBy lengthy DivisionBy Euclidean Algorithm

What is the Relation between LCM and GCF of 26, 52?

The complying with equation have the right to be provided to to express the relation in between LCM (Least typical Multiple) and GCF that 26 and also 52, i.e. GCF × LCM = 26 × 52.