GCF that 9 and also 27 is the largest possible number that divides 9 and 27 specifically without any type of remainder. The components of 9 and 27 are 1, 3, 9 and 1, 3, 9, 27 respectively. There are 3 generally used approaches to discover the GCF that 9 and 27 - Euclidean algorithm, element factorization, and also long division.

You are watching: Greatest common factor of 9 and 27

1.GCF of 9 and 27
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF of 9 and 27 is 9.

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Explanation:

The GCF of two non-zero integers, x(9) and y(27), is the greatest positive essence m(9) that divides both x(9) and y(27) without any kind of remainder.


The approaches to discover the GCF the 9 and also 27 are defined below.

Listing usual FactorsUsing Euclid's AlgorithmLong department Method

GCF the 9 and 27 by Listing typical Factors

Factors that 9: 1, 3, 9Factors of 27: 1, 3, 9, 27

There room 3 common factors the 9 and also 27, that are 1, 3, and 9. Therefore, the greatest common factor the 9 and 27 is 9.

GCF that 9 and 27 by Euclidean Algorithm

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

Here X = 27 and also Y = 9

GCF(27, 9) = GCF(9, 27 mod 9) = GCF(9, 0)GCF(9, 0) = 9 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the worth of GCF of 9 and also 27 is 9.

GCF that 9 and also 27 by lengthy Division

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GCF of 9 and also 27 is the divisor that we get when the remainder becomes 0 after ~ doing long division repeatedly.

Step 2: due to the fact that the remainder = 0, the divisor (9) is the GCF of 9 and also 27.

The matching divisor (9) is the GCF of 9 and 27.

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GCF the 9 and also 27 Examples


Example 1: discover the biggest number the divides 9 and 27 exactly.

Solution:

The biggest number that divides 9 and 27 precisely is their greatest common factor, i.e. GCF the 9 and also 27.⇒ components of 9 and 27:

Factors of 9 = 1, 3, 9Factors that 27 = 1, 3, 9, 27

Therefore, the GCF of 9 and also 27 is 9.


Example 2: uncover the GCF that 9 and also 27, if your LCM is 27.

Solution:

∵ LCM × GCF = 9 × 27⇒ GCF(9, 27) = (9 × 27)/27 = 9Therefore, the greatest common factor that 9 and 27 is 9.


Example 3: The product of 2 numbers is 243. If their GCF is 9, what is their LCM?

Solution:

Given: GCF = 9 and product of numbers = 243∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 243/9Therefore, the LCM is 27.


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FAQs on GCF that 9 and 27

What is the GCF of 9 and also 27?

The GCF of 9 and also 27 is 9. To calculation the GCF the 9 and 27, we need to variable each number (factors the 9 = 1, 3, 9; factors of 27 = 1, 3, 9, 27) and also choose the greatest variable that precisely divides both 9 and also 27, i.e., 9.

How to uncover the GCF of 9 and 27 through Long department Method?

To find the GCF the 9, 27 utilizing long department method, 27 is separated by 9. The equivalent divisor (9) when remainder amounts to 0 is taken together GCF.

What room the techniques to discover GCF that 9 and also 27?

There room three typically used approaches to uncover the GCF that 9 and 27.

By Euclidean AlgorithmBy prime FactorizationBy lengthy Division

What is the Relation between LCM and GCF the 9, 27?

The following equation can be supplied to express the relation between Least typical Multiple (LCM) and GCF the 9 and 27, i.e. GCF × LCM = 9 × 27.

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If the GCF the 27 and also 9 is 9, discover its LCM.

GCF(27, 9) × LCM(27, 9) = 27 × 9Since the GCF of 27 and 9 = 9⇒ 9 × LCM(27, 9) = 243Therefore, LCM = 27☛ GCF Calculator

How to uncover the GCF the 9 and also 27 by prime Factorization?

To find the GCF the 9 and 27, we will find the element factorization of the offered numbers, i.e. 9 = 3 × 3; 27 = 3 × 3 × 3.⇒ because 3, 3 are usual terms in the element factorization that 9 and also 27. Hence, GCF(9, 27) = 3 × 3 = 9☛ element Numbers