GCF that 26 and 14 is the largest possible number the divides 26 and also 14 exactly without any remainder. The factors of 26 and 14 space 1, 2, 13, 26 and 1, 2, 7, 14 respectively. There space 3 frequently used approaches to discover the GCF the 26 and also 14 - Euclidean algorithm, long division, and also prime factorization.

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1.GCF of 26 and 14
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF of 26 and 14 is 2.

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Explanation:

The GCF of two non-zero integers, x(26) and also y(14), is the greatest positive integer m(2) the divides both x(26) and y(14) without any type of remainder.


Let's look in ~ the different methods for finding the GCF that 26 and also 14.

Prime factorization MethodListing typical FactorsLong division Method

GCF the 26 and 14 by element Factorization

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Prime administrate of 26 and also 14 is (2 × 13) and (2 × 7) respectively. Together visible, 26 and also 14 have actually only one typical prime factor i.e. 2. Hence, the GCF of 26 and 14 is 2.

GCF that 26 and 14 through Listing usual Factors

Factors the 26: 1, 2, 13, 26Factors of 14: 1, 2, 7, 14

There room 2 common factors that 26 and also 14, that are 1 and 2. Therefore, the greatest typical factor that 26 and 14 is 2.

GCF the 26 and also 14 by lengthy Division

GCF of 26 and 14 is the divisor that we acquire when the remainder becomes 0 ~ doing long division repeatedly.

Step 2: due to the fact that the remainder ≠ 0, we will divide the divisor of action 1 (14) through the remainder (12).Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 26 and 14.

☛ additionally Check:


GCF the 26 and also 14 Examples


Example 1: discover the greatest number the divides 26 and also 14 exactly.

Solution:

The greatest number the divides 26 and also 14 precisely is your greatest typical factor, i.e. GCF the 26 and 14.⇒ components of 26 and also 14:

Factors of 26 = 1, 2, 13, 26Factors that 14 = 1, 2, 7, 14

Therefore, the GCF that 26 and 14 is 2.


Example 2: For two numbers, GCF = 2 and also LCM = 182. If one number is 26, find the other number.

Solution:

Given: GCF (y, 26) = 2 and LCM (y, 26) = 182∵ GCF × LCM = 26 × (y)⇒ y = (GCF × LCM)/26⇒ y = (2 × 182)/26⇒ y = 14Therefore, the various other number is 14.


Example 3: The product of 2 numbers is 364. If your GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of number = 364∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 364/2Therefore, the LCM is 182.


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FAQs on GCF of 26 and 14

What is the GCF that 26 and also 14?

The GCF that 26 and 14 is 2. To calculate the greatest common factor (GCF) of 26 and 14, we need to factor each number (factors the 26 = 1, 2, 13, 26; determinants of 14 = 1, 2, 7, 14) and choose the greatest factor that exactly divides both 26 and 14, i.e., 2.

If the GCF the 14 and 26 is 2, discover its LCM.

GCF(14, 26) × LCM(14, 26) = 14 × 26Since the GCF of 14 and 26 = 2⇒ 2 × LCM(14, 26) = 364Therefore, LCM = 182☛ Greatest common Factor Calculator

What is the Relation in between LCM and also GCF of 26, 14?

The following equation deserve to be used to express the relation in between LCM and GCF the 26 and also 14, i.e. GCF × LCM = 26 × 14.

How to uncover the GCF of 26 and 14 by element Factorization?

To discover the GCF the 26 and 14, we will uncover the element factorization of the provided numbers, i.e. 26 = 2 × 13; 14 = 2 × 7.⇒ because 2 is the only common prime factor of 26 and also 14. Hence, GCF (26, 14) = 2.☛ element Number

How to discover the GCF that 26 and 14 by Long department Method?

To uncover the GCF of 26, 14 making use of long department method, 26 is separated by 14. The corresponding divisor (2) as soon as remainder amounts to 0 is taken as GCF.

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What space the techniques to uncover GCF the 26 and also 14?

There room three commonly used methods to uncover the GCF the 26 and also 14.