GCF that 24 and also 54 is the largest feasible number that divides 24 and 54 exactly without any remainder. The determinants of 24 and also 54 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 3, 6, 9, 18, 27, 54 respectively. There room 3 typically used techniques to uncover the GCF the 24 and also 54 - Euclidean algorithm, long division, and also prime factorization.

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

Answer: GCF the 24 and 54 is 6.

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Explanation:

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


The methods to uncover the GCF of 24 and also 54 are described below.

Using Euclid's AlgorithmListing typical FactorsPrime administrate Method

GCF of 24 and 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 Y = 24

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

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

GCF the 24 and 54 by Listing common Factors

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

There room 4 usual factors the 24 and 54, that room 1, 2, 3, and 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 54 is (2 × 2 × 2 × 3) and (2 × 3 × 3 × 3) respectively. Together visible, 24 and also 54 have typical prime factors. Hence, the GCF of 24 and 54 is 2 × 3 = 6.

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


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

Solution:

The greatest number that divides 24 and also 54 precisely is your greatest common factor, i.e. GCF that 24 and also 54.⇒ determinants of 24 and 54:

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

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


Example 3: For 2 numbers, GCF = 6 and also 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 various other number is 54.


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FAQs ~ above GCF of 24 and also 54

What is the GCF that 24 and 54?

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

What room the techniques to discover GCF the 24 and 54?

There are three typically used approaches to find the GCF that 24 and 54.

By lengthy DivisionBy Listing typical FactorsBy element Factorization

If the GCF the 54 and also 24 is 6, uncover 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 usual Factor Calculator

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

The adhering to equation deserve to be supplied to express the relation in between Least usual Multiple and GCF of 24 and also 54, i.e. GCF × LCM = 24 × 54.

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How to find the GCF the 24 and also 54 by prime Factorization?

To discover the GCF the 24 and also 54, us will uncover the prime factorization that the given 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 54. Hence, GCF(24, 54) = 2 × 3 = 6☛ element Number

How to discover the GCF of 24 and also 54 by Long department Method?

To find the GCF the 24, 54 using long department method, 54 is split by 24. The equivalent divisor (6) once remainder equals 0 is taken as GCF.