GCF of 4 and 8 is the largest possible number the divides 4 and also 8 precisely without any kind of remainder. The factors of 4 and also 8 space 1, 2, 4 and also 1, 2, 4, 8 respectively. There room 3 typically used approaches to find the GCF that 4 and also 8 - prime factorization, lengthy division, and Euclidean algorithm.

You are watching: What is the greatest common factor of 4 and 8

1.GCF that 4 and also 8
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF of 4 and also 8 is 4.

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Explanation:

The GCF of 2 non-zero integers, x(4) and also y(8), is the best positive creature m(4) that divides both x(4) and y(8) without any remainder.


Let's look in ~ the various methods because that finding the GCF the 4 and also 8.

Prime factorization MethodUsing Euclid's AlgorithmListing typical Factors

GCF that 4 and 8 by element Factorization

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Prime factorization of 4 and also 8 is (2 × 2) and (2 × 2 × 2) respectively. Together visible, 4 and also 8 have usual prime factors. Hence, the GCF of 4 and also 8 is 2 × 2 = 4.

GCF the 4 and also 8 by Euclidean Algorithm

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

Here X = 8 and Y = 4

GCF(8, 4) = GCF(4, 8 mode 4) = GCF(4, 0)GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, whereby X ≠ 0)

Therefore, the value of GCF the 4 and also 8 is 4.

GCF that 4 and also 8 by Listing usual Factors

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Factors that 4: 1, 2, 4Factors the 8: 1, 2, 4, 8

There space 3 usual factors that 4 and also 8, that space 1, 2, and also 4. Therefore, the greatest common factor that 4 and 8 is 4.

☛ likewise Check:


GCF that 4 and also 8 Examples


Example 1: uncover the GCF that 4 and 8, if their LCM is 8.

Solution:

∵ LCM × GCF = 4 × 8⇒ GCF(4, 8) = (4 × 8)/8 = 4Therefore, the greatest common factor of 4 and also 8 is 4.


Example 2: uncover the biggest number that divides 4 and also 8 exactly.

Solution:

The greatest number that divides 4 and 8 precisely is your greatest common factor, i.e. GCF the 4 and 8.⇒ determinants of 4 and 8:

Factors that 4 = 1, 2, 4Factors that 8 = 1, 2, 4, 8

Therefore, the GCF the 4 and 8 is 4.


Example 3: For two numbers, GCF = 4 and LCM = 8. If one number is 4, uncover the various other number.

Solution:

Given: GCF (y, 4) = 4 and also LCM (y, 4) = 8∵ GCF × LCM = 4 × (y)⇒ y = (GCF × LCM)/4⇒ y = (4 × 8)/4⇒ y = 8Therefore, the various other number is 8.


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FAQs on GCF of 4 and 8

What is the GCF that 4 and 8?

The GCF that 4 and 8 is 4. To calculation the greatest typical factor of 4 and 8, we need to variable each number (factors the 4 = 1, 2, 4; components of 8 = 1, 2, 4, 8) and choose the greatest element that specifically divides both 4 and 8, i.e., 4.

How to find the GCF that 4 and 8 by Long department Method?

To uncover the GCF that 4, 8 making use of long division method, 8 is divided by 4. The equivalent divisor (4) once remainder amounts to 0 is taken as GCF.

If the GCF that 8 and 4 is 4, find its LCM.

GCF(8, 4) × LCM(8, 4) = 8 × 4Since the GCF that 8 and also 4 = 4⇒ 4 × LCM(8, 4) = 32Therefore, LCM = 8☛ Greatest usual Factor Calculator

What are the methods to find GCF that 4 and also 8?

There are three generally used techniques to uncover the GCF the 4 and 8.

See more: Do Horizontal Lines Have A Slope Of A Horizontal Line? Finding The Slope Of A Line From A Graph

By prime FactorizationBy long DivisionBy Euclidean Algorithm

What is the Relation between LCM and GCF the 4, 8?

The adhering to equation have the right to be offered to to express the relation in between Least typical Multiple and GCF that 4 and 8, i.e. GCF × LCM = 4 × 8.

How to uncover the GCF of 4 and 8 by prime Factorization?

To discover the GCF of 4 and also 8, us will uncover the prime factorization that the offered numbers, i.e. 4 = 2 × 2; 8 = 2 × 2 × 2.⇒ because 2, 2 are typical terms in the prime factorization that 4 and also 8. Hence, GCF(4, 8) = 2 × 2 = 4☛ What is a element Number?