GCF that 24 and 54 is the largest possible number the divides 24 and also 54 specifically without any type of remainder. The determinants of 24 and also 54 space 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 3, 6, 9, 18, 27, 54 respectively. There room 3 commonly used approaches to discover the GCF of 24 and 54 - Euclidean algorithm, long division, and prime factorization.

You are watching: What is the greatest common factor of 24 and 54

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

Answer: GCF of 24 and also 54 is 6.

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Explanation:

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


The techniques to discover the GCF that 24 and also 54 are described below.

Using Euclid's AlgorithmListing usual FactorsPrime administer Method

GCF that 24 and also 54 by Euclidean Algorithm

As every the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod 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|, wherein X ≠ 0)

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

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

GCF that 24 and also 54 by element Factorization

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

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GCF that 24 and 54 Examples


Example 1: The product of 2 numbers is 1296. If their GCF is 6, what is their LCM?

Solution:

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


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

Solution:

The greatest number the divides 24 and 54 specifically is your greatest common factor, i.e. GCF of 24 and 54.⇒ factors of 24 and 54:

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

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


Example 3: For 2 numbers, GCF = 6 and LCM = 216. If one number is 24, find 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 other number is 54.


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FAQs on GCF the 24 and 54

What is the GCF that 24 and 54?

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

What space the techniques to discover GCF that 24 and also 54?

There are three typically used methods to find the GCF of 24 and 54.

By lengthy DivisionBy Listing common FactorsBy element Factorization

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

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

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

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

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

To uncover the GCF of 24 and also 54, we will uncover the prime factorization of the offered numbers, i.e. 24 = 2 × 2 × 2 × 3; 54 = 2 × 3 × 3 × 3.⇒ because 2, 3 are typical terms in the element factorization the 24 and 54. Hence, GCF(24, 54) = 2 × 3 = 6☛ element Number

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

To uncover the GCF of 24, 54 making use of long department method, 54 is separated by 24. The matching divisor (6) once remainder equates to 0 is taken together GCF.