GCF of 14 and also 28 is the largest feasible number the divides 14 and 28 exactly without any kind of remainder. The determinants of 14 and 28 are 1, 2, 7, 14 and also 1, 2, 4, 7, 14, 28 respectively. There room 3 commonly used methods to discover the GCF the 14 and 28 - lengthy division, Euclidean algorithm, and prime factorization.

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1.GCF that 14 and 28
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF that 14 and also 28 is 14.

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Explanation:

The GCF of two non-zero integers, x(14) and y(28), is the greatest positive essence m(14) that divides both x(14) and y(28) without any kind of remainder.


The techniques to find the GCF the 14 and 28 are described below.

Using Euclid's AlgorithmLong department MethodPrime administer Method

GCF that 14 and also 28 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 = 28 and Y = 14

GCF(28, 14) = GCF(14, 28 mode 14) = GCF(14, 0)GCF(14, 0) = 14 (∵ GCF(X, 0) = |X|, wherein X ≠ 0)

Therefore, the worth of GCF that 14 and also 28 is 14.

GCF the 14 and 28 by lengthy Division

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GCF the 14 and 28 is the divisor that we get when the remainder becomes 0 after ~ doing long division repeatedly.

Step 2: since the remainder = 0, the divisor (14) is the GCF of 14 and 28.

The matching divisor (14) is the GCF that 14 and 28.

GCF of 14 and also 28 by prime Factorization

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Prime administrate of 14 and also 28 is (2 × 7) and (2 × 2 × 7) respectively. Together visible, 14 and also 28 have typical prime factors. Hence, the GCF that 14 and also 28 is 2 × 7 = 14.

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GCF the 14 and 28 Examples


Example 1: For 2 numbers, GCF = 14 and also LCM = 28. If one number is 28, find the other number.

Solution:

Given: GCF (y, 28) = 14 and LCM (y, 28) = 28∵ GCF × LCM = 28 × (y)⇒ y = (GCF × LCM)/28⇒ y = (14 × 28)/28⇒ y = 14Therefore, the other number is 14.


Example 2: uncover the GCF the 14 and 28, if their LCM is 28.

Solution:

∵ LCM × GCF = 14 × 28⇒ GCF(14, 28) = (14 × 28)/28 = 14Therefore, the greatest typical factor that 14 and also 28 is 14.


Example 3: find the greatest number that divides 14 and also 28 exactly.

Solution:

The biggest number the divides 14 and also 28 specifically is their greatest common factor, i.e. GCF that 14 and 28.⇒ components of 14 and 28:

Factors that 14 = 1, 2, 7, 14Factors that 28 = 1, 2, 4, 7, 14, 28

Therefore, the GCF of 14 and 28 is 14.


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FAQs on GCF that 14 and 28

What is the GCF the 14 and also 28?

The GCF that 14 and also 28 is 14. To calculate the GCF of 14 and also 28, we need to factor each number (factors that 14 = 1, 2, 7, 14; factors of 28 = 1, 2, 4, 7, 14, 28) and also choose the greatest aspect that specifically divides both 14 and 28, i.e., 14.

What room the approaches to find GCF the 14 and 28?

There room three commonly used methods to uncover the GCF the 14 and 28.

By prime FactorizationBy lengthy DivisionBy Listing common Factors

If the GCF that 28 and also 14 is 14, uncover its LCM.

GCF(28, 14) × LCM(28, 14) = 28 × 14Since the GCF of 28 and 14 = 14⇒ 14 × LCM(28, 14) = 392Therefore, LCM = 28☛ GCF Calculator

How to find the GCF of 14 and also 28 by element Factorization?

To uncover the GCF the 14 and also 28, we will discover the prime factorization the the provided numbers, i.e. 14 = 2 × 7; 28 = 2 × 2 × 7.⇒ due to the fact that 2, 7 are usual terms in the prime factorization that 14 and also 28. Hence, GCF(14, 28) = 2 × 7 = 14☛ What are Prime Numbers?

What is the Relation in between LCM and also GCF that 14, 28?

The adhering to equation have the right to be used to express the relation in between Least usual Multiple and GCF that 14 and 28, i.e. GCF × LCM = 14 × 28.

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How to discover the GCF that 14 and also 28 through Long division Method?

To find the GCF the 14, 28 using long department method, 28 is separated by 14. The equivalent divisor (14) once remainder equals 0 is taken as GCF.