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

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

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

Answer: GCF that 24 and 54 is 6.

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Explanation:

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


The approaches to uncover the GCF of 24 and also 54 are explained below.

Using Euclid's AlgorithmListing usual FactorsPrime administrate Method

GCF of 24 and also 54 through Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mode Y)where X > Y and 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 mod 6) = GCF(6, 0)GCF(6, 0) = 6 (∵ GCF(X, 0) = |X|, where X ≠ 0)

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

GCF the 24 and also 54 through Listing common 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 typical factors that 24 and also 54, that room 1, 2, 3, and also 6. Therefore, the greatest typical factor the 24 and 54 is 6.

GCF that 24 and 54 by prime Factorization

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

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


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

Solution:

The greatest number that divides 24 and also 54 precisely is their greatest typical factor, i.e. GCF of 24 and 54.⇒ components of 24 and 54:

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

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


Example 3: For two numbers, GCF = 6 and also LCM = 216. If one number is 24, uncover the other number.

Solution:

Given: GCF (z, 24) = 6 and also 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 top top GCF that 24 and also 54

What is the GCF of 24 and also 54?

The GCF that 24 and also 54 is 6. To calculate the greatest typical factor (GCF) that 24 and also 54, we need to aspect 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 also choose the greatest aspect that precisely divides both 24 and 54, i.e., 6.

What space the approaches to uncover GCF of 24 and 54?

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

By lengthy DivisionBy Listing typical FactorsBy element Factorization

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

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

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

The following equation can be used to refer the relation in between Least usual Multiple and GCF of 24 and 54, i.e. GCF × LCM = 24 × 54.

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

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

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

To find the GCF that 24, 54 using long division method, 54 is divided by 24. The corresponding divisor (6) once remainder equals 0 is taken as GCF.