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

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

Answer: GCF of 24 and 54 is 6.

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Explanation:

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


The approaches to find the GCF the 24 and also 54 are defined below.

Using Euclid's AlgorithmListing typical FactorsPrime administer Method

GCF that 24 and also 54 by Euclidean Algorithm

As every 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 mode 6) = GCF(6, 0)GCF(6, 0) = 6 (∵ GCF(X, 0) = |X|, whereby X ≠ 0)

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

GCF that 24 and 54 by Listing usual Factors

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

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

GCF of 24 and also 54 by element Factorization

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Prime factorization of 24 and also 54 is (2 × 2 × 2 × 3) and also (2 × 3 × 3 × 3) respectively. As visible, 24 and 54 have typical prime factors. Hence, the GCF that 24 and 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 your 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: uncover the best number that divides 24 and 54 exactly.

Solution:

The best number the divides 24 and also 54 exactly is their greatest typical factor, i.e. GCF of 24 and 54.⇒ factors 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 of 24 and also 54 is 6.


Example 3: For 2 numbers, GCF = 6 and LCM = 216. If one number is 24, uncover the 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 top top GCF the 24 and also 54

What is the GCF that 24 and 54?

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

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

There room three generally used methods to uncover the GCF that 24 and also 54.

By lengthy DivisionBy Listing usual FactorsBy prime Factorization

If the GCF the 54 and also 24 is 6, discover 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 GCF that 24, 54?

The following equation have the right to be used to to express the relation between Least common Multiple and also GCF that 24 and also 54, i.e. GCF × LCM = 24 × 54.

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

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

How to uncover the GCF of 24 and 54 by Long division Method?

To discover the GCF the 24, 54 making use of long department method, 54 is separated by 24. The matching divisor (6) when remainder equals 0 is taken together GCF.