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GCF of 25 and 75

GCF of 25 and 75 is the largest possible number that divides 25 and 75 exactly without any remainder. The factors of 25 and 75 are 1, 5, 25 and 1, 3, 5, 15, 25, 75 respectively. There are 3 commonly used methods to find the GCF of 25 and 75 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 25 and 75
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 25 and 75?

Answer: GCF of 25 and 75 is 25.

Explanation:

The GCF of two non-zero integers, x(25) and y(75), is the greatest positive integer m(25) that divides both x(25) and y(75) without any remainder.

Methods to Find GCF of 25 and 75

Let's look at the different methods for finding the GCF of 25 and 75.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 25 and 75 by Prime Factorization

Prime factorization of 25 and 75 is (5 × 5) and (3 × 5 × 5) respectively. As visible, 25 and 75 have common prime factors. Hence, the GCF of 25 and 75 is 5 × 5 = 25.

GCF of 25 and 75 by Long Division

GCF of 25 and 75 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 75 (larger number) by 25 (smaller number).
Step 2: Since the remainder = 0, the divisor (25) is the GCF of 25 and 75.

The corresponding divisor (25) is the GCF of 25 and 75.

GCF of 25 and 75 by Listing Common Factors

Factors of 25: 1, 5, 25
Factors of 75: 1, 3, 5, 15, 25, 75

There are 3 common factors of 25 and 75, that are 1, 5, and 25. Therefore, the greatest common factor of 25 and 75 is 25.

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GCF of 25 and 75 Examples

Example 1: The product of two numbers is 1875. If their GCF is 25, what is their LCM?

Solution:

Given: GCF = 25 and product of numbers = 1875
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1875/25
Therefore, the LCM is 75.
Example 2: For two numbers, GCF = 25 and LCM = 75. If one number is 25, find the other number.

Solution:

Given: GCF (y, 25) = 25 and LCM (y, 25) = 75
∵ GCF × LCM = 25 × (y)
⇒ y = (GCF × LCM)/25
⇒ y = (25 × 75)/25
⇒ y = 75
Therefore, the other number is 75.
Example 3: Find the greatest number that divides 25 and 75 exactly.

Solution:

The greatest number that divides 25 and 75 exactly is their greatest common factor, i.e. GCF of 25 and 75.
⇒ Factors of 25 and 75:
- Factors of 25 = 1, 5, 25
- Factors of 75 = 1, 3, 5, 15, 25, 75
Therefore, the GCF of 25 and 75 is 25.

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FAQs on GCF of 25 and 75

What is the GCF of 25 and 75?

The GCF of 25 and 75 is 25. To calculate the GCF (Greatest Common Factor) of 25 and 75, we need to factor each number (factors of 25 = 1, 5, 25; factors of 75 = 1, 3, 5, 15, 25, 75) and choose the greatest factor that exactly divides both 25 and 75, i.e., 25.

What are the Methods to Find GCF of 25 and 75?

There are three commonly used methods to find the GCF of 25 and 75.

By Euclidean Algorithm
By Prime Factorization
By Long Division

If the GCF of 75 and 25 is 25, Find its LCM.

GCF(75, 25) × LCM(75, 25) = 75 × 25
Since the GCF of 75 and 25 = 25
⇒ 25 × LCM(75, 25) = 1875
Therefore, LCM = 75
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How to Find the GCF of 25 and 75 by Prime Factorization?

To find the GCF of 25 and 75, we will find the prime factorization of the given numbers, i.e. 25 = 5 × 5; 75 = 3 × 5 × 5.
⇒ Since 5, 5 are common terms in the prime factorization of 25 and 75. Hence, GCF(25, 75) = 5 × 5 = 25
☛ What is a Prime Number?

How to Find the GCF of 25 and 75 by Long Division Method?

To find the GCF of 25, 75 using long division method, 75 is divided by 25. The corresponding divisor (25) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 25, 75?

The following equation can be used to express the relation between LCM and GCF of 25 and 75, i.e. GCF × LCM = 25 × 75.

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