GCF the 24 and also 54 is the largest possible number that divides 24 and 54 precisely without any kind of remainder. The components of 24 and 54 space 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 3, 6, 9, 18, 27, 54 respectively. There space 3 typically used methods to uncover the GCF of 24 and 54 - Euclidean algorithm, long division, and prime factorization.

You are watching: What is the gcf of 24 and 54

1.GCF of 24 and also 54
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF of 24 and 54 is 6.

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Explanation:

The GCF of 2 non-zero integers, x(24) and y(54), is the greatest positive integer m(6) that divides both x(24) and y(54) without any type of remainder.


The methods to discover the GCF the 24 and also 54 are explained below.

Using Euclid's AlgorithmListing typical FactorsPrime administrate Method

GCF that 24 and also 54 by Euclidean Algorithm

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

Here X = 54 and also Y = 24

GCF(54, 24) = GCF(24, 54 mod 24) = GCF(24, 6)GCF(24, 6) = GCF(6, 24 mode 6) = GCF(6, 0)GCF(6, 0) = 6 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 24 and also 54 is 6.

GCF the 24 and also 54 by Listing typical Factors

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Factors that 24: 1, 2, 3, 4, 6, 8, 12, 24Factors the 54: 1, 2, 3, 6, 9, 18, 27, 54

There room 4 usual factors that 24 and also 54, that space 1, 2, 3, and also 6. Therefore, the greatest typical factor of 24 and also 54 is 6.

GCF the 24 and 54 by prime Factorization

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Prime administer of 24 and also 54 is (2 × 2 × 2 × 3) and (2 × 3 × 3 × 3) respectively. As visible, 24 and 54 have usual prime factors. Hence, the GCF that 24 and also 54 is 2 × 3 = 6.

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GCF that 24 and also 54 Examples


Example 1: The product of two numbers is 1296. If their GCF is 6, what is their LCM?

Solution:

Given: GCF = 6 and product of numbers = 1296∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 1296/6Therefore, the LCM is 216.


Example 2: find the best number the divides 24 and also 54 exactly.

Solution:

The greatest number the divides 24 and also 54 exactly is their greatest common factor, i.e. GCF of 24 and 54.⇒ components of 24 and 54:

Factors that 24 = 1, 2, 3, 4, 6, 8, 12, 24Factors the 54 = 1, 2, 3, 6, 9, 18, 27, 54

Therefore, the GCF of 24 and also 54 is 6.


Example 3: For 2 numbers, GCF = 6 and LCM = 216. If one number is 24, discover the various other number.

Solution:

Given: GCF (z, 24) = 6 and LCM (z, 24) = 216∵ GCF × LCM = 24 × (z)⇒ z = (GCF × LCM)/24⇒ z = (6 × 216)/24⇒ z = 54Therefore, the various other number is 54.


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FAQs top top GCF the 24 and also 54

What is the GCF that 24 and 54?

The GCF that 24 and 54 is 6. To calculate the greatest usual factor (GCF) the 24 and also 54, we need to aspect each number (factors that 24 = 1, 2, 3, 4, 6, 8, 12, 24; components of 54 = 1, 2, 3, 6, 9, 18, 27, 54) and choose the greatest variable that exactly divides both 24 and also 54, i.e., 6.

What are the approaches to uncover GCF the 24 and 54?

There space three typically used approaches to discover the GCF of 24 and also 54.

By lengthy DivisionBy Listing typical FactorsBy element Factorization

If the GCF the 54 and 24 is 6, find its LCM.

GCF(54, 24) × LCM(54, 24) = 54 × 24Since the GCF of 54 and 24 = 6⇒ 6 × LCM(54, 24) = 1296Therefore, LCM = 216☛ Greatest typical Factor Calculator

What is the Relation between LCM and also GCF the 24, 54?

The adhering to equation can be offered to refer the relation between Least typical Multiple and GCF that 24 and also 54, i.e. GCF × LCM = 24 × 54.

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How to uncover the GCF of 24 and also 54 by element Factorization?

To discover the GCF the 24 and also 54, us will discover the element factorization of the provided numbers, i.e. 24 = 2 × 2 × 2 × 3; 54 = 2 × 3 × 3 × 3.⇒ due to the fact that 2, 3 are usual terms in the prime factorization that 24 and also 54. Hence, GCF(24, 54) = 2 × 3 = 6☛ element Number

How to find the GCF the 24 and 54 through Long division Method?

To uncover the GCF the 24, 54 using long division method, 54 is separated by 24. The matching divisor (6) once remainder equals 0 is taken as GCF.