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GCF of 9 and 27

GCF of 9 and 27 is the largest possible number that divides 9 and 27 exactly without any remainder. The factors of 9 and 27 are 1, 3, 9 and 1, 3, 9, 27 respectively. There are 3 commonly used methods to find the GCF of 9 and 27 - Euclidean algorithm, prime factorization, and long division.

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

What is GCF of 9 and 27?

Answer: GCF of 9 and 27 is 9.

Explanation:

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

Methods to Find GCF of 9 and 27

The methods to find the GCF of 9 and 27 are explained below.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

GCF of 9 and 27 by Listing Common Factors

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

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

GCF of 9 and 27 by Euclidean Algorithm

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

Here X = 27 and 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 value of GCF of 9 and 27 is 9.

GCF of 9 and 27 by Long Division

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

Step 1: Divide 27 (larger number) by 9 (smaller number).
Step 2: Since the remainder = 0, the divisor (9) is the GCF of 9 and 27.

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

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GCF of 9 and 27 Examples

Example 1: Find the greatest number that divides 9 and 27 exactly.

Solution:

The greatest number that divides 9 and 27 exactly is their greatest common factor, i.e. GCF of 9 and 27.
⇒ Factors of 9 and 27:
- Factors of 9 = 1, 3, 9
- Factors of 27 = 1, 3, 9, 27
Therefore, the GCF of 9 and 27 is 9.
Example 2: Find the GCF of 9 and 27, if their LCM is 27.

Solution:

∵ LCM × GCF = 9 × 27
⇒ GCF(9, 27) = (9 × 27)/27 = 9
Therefore, the greatest common factor of 9 and 27 is 9.
Example 3: The product of two numbers is 243. If their GCF is 9, what is their LCM?

Solution:

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

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FAQs on GCF of 9 and 27

What is the GCF of 9 and 27?

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

How to Find the GCF of 9 and 27 by Long Division Method?

To find the GCF of 9, 27 using long division method, 27 is divided by 9. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 9 and 27?

There are three commonly used methods to find the GCF of 9 and 27.

By Euclidean Algorithm
By Prime Factorization
By Long Division

What is the Relation Between LCM and GCF of 9, 27?

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

If the GCF of 27 and 9 is 9, Find its LCM.

GCF(27, 9) × LCM(27, 9) = 27 × 9
Since the GCF of 27 and 9 = 9
⇒ 9 × LCM(27, 9) = 243
Therefore, LCM = 27
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How to Find the GCF of 9 and 27 by Prime Factorization?

To find the GCF of 9 and 27, we will find the prime factorization of the given numbers, i.e. 9 = 3 × 3; 27 = 3 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 9 and 27. Hence, GCF(9, 27) = 3 × 3 = 9
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