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GCF of 25 and 50

GCF of 25 and 50 is the largest possible number that divides 25 and 50 exactly without any remainder. The factors of 25 and 50 are 1, 5, 25 and 1, 2, 5, 10, 25, 50 respectively. There are 3 commonly used methods to find the GCF of 25 and 50 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 25 and 50
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 25 and 50?

Answer: GCF of 25 and 50 is 25.

Explanation:

The GCF of two non-zero integers, x(25) and y(50), is the greatest positive integer m(25) that divides both x(25) and y(50) without any remainder.

Methods to Find GCF of 25 and 50

Let's look at the different methods for finding the GCF of 25 and 50.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 25 and 50 by Prime Factorization

Prime factorization of 25 and 50 is (5 × 5) and (2 × 5 × 5) respectively. As visible, 25 and 50 have common prime factors. Hence, the GCF of 25 and 50 is 5 × 5 = 25.

GCF of 25 and 50 by Listing Common Factors

Factors of 25: 1, 5, 25
Factors of 50: 1, 2, 5, 10, 25, 50

There are 3 common factors of 25 and 50, that are 1, 5, and 25. Therefore, the greatest common factor of 25 and 50 is 25.

GCF of 25 and 50 by Long Division

GCF of 25 and 50 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 50 (larger number) by 25 (smaller number).
Step 2: Since the remainder = 0, the divisor (25) is the GCF of 25 and 50.

The corresponding divisor (25) is the GCF of 25 and 50.

☛ Also Check:

GCF of 25 and 50 Examples

Example 1: For two numbers, GCF = 25 and LCM = 50. If one number is 25, find the other number.

Solution:

Given: GCF (z, 25) = 25 and LCM (z, 25) = 50
∵ GCF × LCM = 25 × (z)
⇒ z = (GCF × LCM)/25
⇒ z = (25 × 50)/25
⇒ z = 50
Therefore, the other number is 50.
Example 2: Find the GCF of 25 and 50, if their LCM is 50.

Solution:

∵ LCM × GCF = 25 × 50
⇒ GCF(25, 50) = (25 × 50)/50 = 25
Therefore, the greatest common factor of 25 and 50 is 25.
Example 3: The product of two numbers is 1250. If their GCF is 25, what is their LCM?

Solution:

Given: GCF = 25 and product of numbers = 1250
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1250/25
Therefore, the LCM is 50.

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FAQs on GCF of 25 and 50

What is the GCF of 25 and 50?

The GCF of 25 and 50 is 25. To calculate the greatest common factor (GCF) of 25 and 50, we need to factor each number (factors of 25 = 1, 5, 25; factors of 50 = 1, 2, 5, 10, 25, 50) and choose the greatest factor that exactly divides both 25 and 50, i.e., 25.

If the GCF of 50 and 25 is 25, Find its LCM.

GCF(50, 25) × LCM(50, 25) = 50 × 25
Since the GCF of 50 and 25 = 25
⇒ 25 × LCM(50, 25) = 1250
Therefore, LCM = 50
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 25, 50?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 25 and 50, i.e. GCF × LCM = 25 × 50.

How to Find the GCF of 25 and 50 by Prime Factorization?

To find the GCF of 25 and 50, we will find the prime factorization of the given numbers, i.e. 25 = 5 × 5; 50 = 2 × 5 × 5.
⇒ Since 5, 5 are common terms in the prime factorization of 25 and 50. Hence, GCF(25, 50) = 5 × 5 = 25
☛ Prime Number

How to Find the GCF of 25 and 50 by Long Division Method?

To find the GCF of 25, 50 using long division method, 50 is divided by 25. The corresponding divisor (25) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 25 and 50?

There are three commonly used methods to find the GCF of 25 and 50.

By Long Division
By Euclidean Algorithm
By Prime Factorization

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