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GCF of 9 and 25

GCF of 9 and 25 is the largest possible number that divides 9 and 25 exactly without any remainder. The factors of 9 and 25 are 1, 3, 9 and 1, 5, 25 respectively. There are 3 commonly used methods to find the GCF of 9 and 25 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 9 and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 9 and 25?

Answer: GCF of 9 and 25 is 1.

Explanation:

The GCF of two non-zero integers, x(9) and y(25), is the greatest positive integer m(1) that divides both x(9) and y(25) without any remainder.

Methods to Find GCF of 9 and 25

Let's look at the different methods for finding the GCF of 9 and 25.

Prime Factorization Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 9 and 25 by Prime Factorization

Prime factorization of 9 and 25 is (3 × 3) and (5 × 5) respectively. As visible, there are no common prime factors between 9 and 25, i.e. they are co-prime. Hence, the GCF of 9 and 25 will be 1.

GCF of 9 and 25 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 = 25 and Y = 9

GCF(25, 9) = GCF(9, 25 mod 9) = GCF(9, 7)
GCF(9, 7) = GCF(7, 9 mod 7) = GCF(7, 2)
GCF(7, 2) = GCF(2, 7 mod 2) = GCF(2, 1)
GCF(2, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 9 and 25 is 1.

GCF of 9 and 25 by Listing Common Factors

Factors of 9: 1, 3, 9
Factors of 25: 1, 5, 25

Since, 1 is the only common factor between 9 and 25. The Greatest Common Factor of 9 and 25 is 1.

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GCF of 9 and 25 Examples

Example 1: Find the GCF of 9 and 25, if their LCM is 225.

Solution:

∵ LCM × GCF = 9 × 25
⇒ GCF(9, 25) = (9 × 25)/225 = 1
Therefore, the greatest common factor of 9 and 25 is 1.
Example 2: The product of two numbers is 225. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 225
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 225/1
Therefore, the LCM is 225.
Example 3: For two numbers, GCF = 1 and LCM = 225. If one number is 9, find the other number.

Solution:

Given: GCF (x, 9) = 1 and LCM (x, 9) = 225
∵ GCF × LCM = 9 × (x)
⇒ x = (GCF × LCM)/9
⇒ x = (1 × 225)/9
⇒ x = 25
Therefore, the other number is 25.

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FAQs on GCF of 9 and 25

What is the GCF of 9 and 25?

The GCF of 9 and 25 is 1. To calculate the greatest common factor (GCF) of 9 and 25, we need to factor each number (factors of 9 = 1, 3, 9; factors of 25 = 1, 5, 25) and choose the greatest factor that exactly divides both 9 and 25, i.e., 1.

What are the Methods to Find GCF of 9 and 25?

There are three commonly used methods to find the GCF of 9 and 25.

By Long Division
By Listing Common Factors
By Prime Factorization

How to Find the GCF of 9 and 25 by Long Division Method?

To find the GCF of 9, 25 using long division method, 25 is divided by 9. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 9, 25?

The following equation can be used to express the relation between Least Common Multiple and GCF of 9 and 25, i.e. GCF × LCM = 9 × 25.

If the GCF of 25 and 9 is 1, Find its LCM.

GCF(25, 9) × LCM(25, 9) = 25 × 9
Since the GCF of 25 and 9 = 1
⇒ 1 × LCM(25, 9) = 225
Therefore, LCM = 225
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How to Find the GCF of 9 and 25 by Prime Factorization?

To find the GCF of 9 and 25, we will find the prime factorization of the given numbers, i.e. 9 = 3 × 3; 25 = 5 × 5.
⇒ There is no common prime factor for 9 and 25. Hence, GCF (9, 25) = 1.
☛ What are Prime Numbers?

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