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GCF of 9 and 45

GCF of 9 and 45 is the largest possible number that divides 9 and 45 exactly without any remainder. The factors of 9 and 45 are 1, 3, 9 and 1, 3, 5, 9, 15, 45 respectively. There are 3 commonly used methods to find the GCF of 9 and 45 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 9 and 45
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 9 and 45?

Answer: GCF of 9 and 45 is 9.

Explanation:

The GCF of two non-zero integers, x(9) and y(45), is the greatest positive integer m(9) that divides both x(9) and y(45) without any remainder.

Methods to Find GCF of 9 and 45

The methods to find the GCF of 9 and 45 are explained below.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

GCF of 9 and 45 by Listing Common Factors

Factors of 9: 1, 3, 9
Factors of 45: 1, 3, 5, 9, 15, 45

There are 3 common factors of 9 and 45, that are 1, 3, and 9. Therefore, the greatest common factor of 9 and 45 is 9.

GCF of 9 and 45 by Prime Factorization

Prime factorization of 9 and 45 is (3 × 3) and (3 × 3 × 5) respectively. As visible, 9 and 45 have common prime factors. Hence, the GCF of 9 and 45 is 3 × 3 = 9.

GCF of 9 and 45 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 = 45 and Y = 9

GCF(45, 9) = GCF(9, 45 mod 9) = GCF(9, 0)
GCF(9, 0) = 9 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 9 and 45 is 9.

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GCF of 9 and 45 Examples

Example 1: Find the greatest number that divides 9 and 45 exactly.

Solution:

The greatest number that divides 9 and 45 exactly is their greatest common factor, i.e. GCF of 9 and 45.
⇒ Factors of 9 and 45:
- Factors of 9 = 1, 3, 9
- Factors of 45 = 1, 3, 5, 9, 15, 45
Therefore, the GCF of 9 and 45 is 9.
Example 2: Find the GCF of 9 and 45, if their LCM is 45.

Solution:

∵ LCM × GCF = 9 × 45
⇒ GCF(9, 45) = (9 × 45)/45 = 9
Therefore, the greatest common factor of 9 and 45 is 9.
Example 3: The product of two numbers is 405. If their GCF is 9, what is their LCM?

Solution:

Given: GCF = 9 and product of numbers = 405
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 405/9
Therefore, the LCM is 45.

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FAQs on GCF of 9 and 45

What is the GCF of 9 and 45?

The GCF of 9 and 45 is 9. To calculate the GCF (Greatest Common Factor) of 9 and 45, we need to factor each number (factors of 9 = 1, 3, 9; factors of 45 = 1, 3, 5, 9, 15, 45) and choose the greatest factor that exactly divides both 9 and 45, i.e., 9.

If the GCF of 45 and 9 is 9, Find its LCM.

GCF(45, 9) × LCM(45, 9) = 45 × 9
Since the GCF of 45 and 9 = 9
⇒ 9 × LCM(45, 9) = 405
Therefore, LCM = 45
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 9 and 45?

There are three commonly used methods to find the GCF of 9 and 45.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the GCF of 9 and 45 by Long Division Method?

To find the GCF of 9, 45 using long division method, 45 is divided by 9. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

How to Find the GCF of 9 and 45 by Prime Factorization?

To find the GCF of 9 and 45, we will find the prime factorization of the given numbers, i.e. 9 = 3 × 3; 45 = 3 × 3 × 5.
⇒ Since 3, 3 are common terms in the prime factorization of 9 and 45. Hence, GCF(9, 45) = 3 × 3 = 9
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 9, 45?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 9 and 45, i.e. GCF × LCM = 9 × 45.

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