GCF of 4 and 20 is the largest feasible number that divides 4 and also 20 exactly without any type of remainder. The factors of 4 and 20 space 1, 2, 4 and also 1, 2, 4, 5, 10, 20 respectively. There space 3 generally used approaches to find the GCF of 4 and also 20 - Euclidean algorithm, long division, and prime factorization.

You are watching: Greatest common factor of 4 and 20

1.GCF of 4 and also 20
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF the 4 and also 20 is 4.

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Explanation:

The GCF of 2 non-zero integers, x(4) and also y(20), is the greatest positive integer m(4) the divides both x(4) and also y(20) without any remainder.


Let's look in ~ the various methods because that finding the GCF of 4 and also 20.

Using Euclid's AlgorithmLong department MethodListing typical Factors

GCF of 4 and 20 through Euclidean Algorithm

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

Here X = 20 and Y = 4

GCF(20, 4) = GCF(4, 20 mod 4) = GCF(4, 0)GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF the 4 and also 20 is 4.

GCF the 4 and also 20 by long Division

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GCF that 4 and 20 is the divisor that we get 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 (4) is the GCF of 4 and 20.

The corresponding divisor (4) is the GCF that 4 and 20.

GCF that 4 and also 20 by Listing common Factors

Factors of 4: 1, 2, 4Factors the 20: 1, 2, 4, 5, 10, 20

There are 3 usual factors of 4 and 20, that are 1, 2, and 4. Therefore, the greatest usual factor of 4 and also 20 is 4.

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GCF that 4 and 20 Examples


Example 1: uncover the GCF of 4 and 20, if your LCM is 20.

Solution:

∵ LCM × GCF = 4 × 20⇒ GCF(4, 20) = (4 × 20)/20 = 4Therefore, the greatest usual factor that 4 and also 20 is 4.


Example 2: The product of 2 numbers is 80. If their GCF is 4, what is your LCM?

Solution:

Given: GCF = 4 and also product of numbers = 80∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 80/4Therefore, the LCM is 20.


Example 3: For two numbers, GCF = 4 and LCM = 20. If one number is 4, find the various other number.

Solution:

Given: GCF (z, 4) = 4 and LCM (z, 4) = 20∵ GCF × LCM = 4 × (z)⇒ z = (GCF × LCM)/4⇒ z = (4 × 20)/4⇒ z = 20Therefore, the other number is 20.


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FAQs on GCF the 4 and 20

What is the GCF that 4 and 20?

The GCF of 4 and 20 is 4. To calculation the GCF (Greatest usual Factor) that 4 and also 20, we require to factor each number (factors the 4 = 1, 2, 4; components of 20 = 1, 2, 4, 5, 10, 20) and choose the greatest aspect that exactly divides both 4 and also 20, i.e., 4.

How to discover the GCF of 4 and also 20 by Long department Method?

To uncover the GCF of 4, 20 utilizing long division method, 20 is separated by 4. The corresponding divisor (4) as soon as remainder amounts to 0 is taken together GCF.

How to uncover the GCF of 4 and 20 by prime Factorization?

To uncover the GCF the 4 and 20, we will uncover the prime factorization that the given numbers, i.e. 4 = 2 × 2; 20 = 2 × 2 × 5.⇒ due to the fact that 2, 2 are common terms in the prime factorization the 4 and also 20. Hence, GCF(4, 20) = 2 × 2 = 4☛ element Number

What room the techniques to uncover GCF that 4 and 20?

There space three commonly used techniques to uncover the GCF that 4 and 20.

By lengthy DivisionBy Listing usual FactorsBy element Factorization

What is the Relation between LCM and also GCF the 4, 20?

The following equation deserve to be provided to to express the relation between Least typical Multiple and also GCF the 4 and 20, i.e. GCF × LCM = 4 × 20.

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If the GCF that 20 and also 4 is 4, discover its LCM.

GCF(20, 4) × LCM(20, 4) = 20 × 4Since the GCF of 20 and also 4 = 4⇒ 4 × LCM(20, 4) = 80Therefore, LCM = 20☛ GCF Calculator