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GCF of 25 and 45

GCF of 25 and 45 is the largest possible number that divides 25 and 45 exactly without any remainder. The factors of 25 and 45 are 1, 5, 25 and 1, 3, 5, 9, 15, 45 respectively. There are 3 commonly used methods to find the GCF of 25 and 45 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 25 and 45
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 25 and 45?

Answer: GCF of 25 and 45 is 5.

Explanation:

The GCF of two non-zero integers, x(25) and y(45), is the greatest positive integer m(5) that divides both x(25) and y(45) without any remainder.

Methods to Find GCF of 25 and 45

Let's look at the different methods for finding the GCF of 25 and 45.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 25 and 45 by Long Division

GCF of 25 and 45 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 45 (larger number) by 25 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (25) by the remainder (20).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 25 and 45.

GCF of 25 and 45 by Listing Common Factors

Factors of 25: 1, 5, 25
Factors of 45: 1, 3, 5, 9, 15, 45

There are 2 common factors of 25 and 45, that are 1 and 5. Therefore, the greatest common factor of 25 and 45 is 5.

GCF of 25 and 45 by Prime Factorization

Prime factorization of 25 and 45 is (5 × 5) and (3 × 3 × 5) respectively. As visible, 25 and 45 have only one common prime factor i.e. 5. Hence, the GCF of 25 and 45 is 5.

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GCF of 25 and 45 Examples

Example 1: The product of two numbers is 1125. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 1125
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1125/5
Therefore, the LCM is 225.
Example 2: For two numbers, GCF = 5 and LCM = 225. If one number is 45, find the other number.

Solution:

Given: GCF (y, 45) = 5 and LCM (y, 45) = 225
∵ GCF × LCM = 45 × (y)
⇒ y = (GCF × LCM)/45
⇒ y = (5 × 225)/45
⇒ y = 25
Therefore, the other number is 25.
Example 3: Find the GCF of 25 and 45, if their LCM is 225.

Solution:

∵ LCM × GCF = 25 × 45
⇒ GCF(25, 45) = (25 × 45)/225 = 5
Therefore, the greatest common factor of 25 and 45 is 5.

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FAQs on GCF of 25 and 45

What is the GCF of 25 and 45?

The GCF of 25 and 45 is 5. To calculate the greatest common factor (GCF) of 25 and 45, we need to factor each number (factors of 25 = 1, 5, 25; factors of 45 = 1, 3, 5, 9, 15, 45) and choose the greatest factor that exactly divides both 25 and 45, i.e., 5.

How to Find the GCF of 25 and 45 by Prime Factorization?

To find the GCF of 25 and 45, we will find the prime factorization of the given numbers, i.e. 25 = 5 × 5; 45 = 3 × 3 × 5.
⇒ Since 5 is the only common prime factor of 25 and 45. Hence, GCF (25, 45) = 5.
☛ Prime Number

If the GCF of 45 and 25 is 5, Find its LCM.

GCF(45, 25) × LCM(45, 25) = 45 × 25
Since the GCF of 45 and 25 = 5
⇒ 5 × LCM(45, 25) = 1125
Therefore, LCM = 225
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 25, 45?

The following equation can be used to express the relation between Least Common Multiple and GCF of 25 and 45, i.e. GCF × LCM = 25 × 45.

What are the Methods to Find GCF of 25 and 45?

There are three commonly used methods to find the GCF of 25 and 45.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the GCF of 25 and 45 by Long Division Method?

To find the GCF of 25, 45 using long division method, 45 is divided by 25. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

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