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GCF of 25 and 100

GCF of 25 and 100 is the largest possible number that divides 25 and 100 exactly without any remainder. The factors of 25 and 100 are 1, 5, 25 and 1, 2, 4, 5, 10, 20, 25, 50, 100 respectively. There are 3 commonly used methods to find the GCF of 25 and 100 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 25 and 100
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 25 and 100?

Answer: GCF of 25 and 100 is 25.

Explanation:

The GCF of two non-zero integers, x(25) and y(100), is the greatest positive integer m(25) that divides both x(25) and y(100) without any remainder.

Methods to Find GCF of 25 and 100

Let's look at the different methods for finding the GCF of 25 and 100.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

GCF of 25 and 100 by Long Division

GCF of 25 and 100 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 100 (larger number) by 25 (smaller number).
Step 2: Since the remainder = 0, the divisor (25) is the GCF of 25 and 100.

The corresponding divisor (25) is the GCF of 25 and 100.

GCF of 25 and 100 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 = 100 and Y = 25

GCF(100, 25) = GCF(25, 100 mod 25) = GCF(25, 0)
GCF(25, 0) = 25 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 25 and 100 is 25.

GCF of 25 and 100 by Prime Factorization

Prime factorization of 25 and 100 is (5 × 5) and (2 × 2 × 5 × 5) respectively. As visible, 25 and 100 have common prime factors. Hence, the GCF of 25 and 100 is 5 × 5 = 25.

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GCF of 25 and 100 Examples

Example 1: The product of two numbers is 2500. If their GCF is 25, what is their LCM?

Solution:

Given: GCF = 25 and product of numbers = 2500
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2500/25
Therefore, the LCM is 100.
Example 2: Find the greatest number that divides 25 and 100 exactly.

Solution:

The greatest number that divides 25 and 100 exactly is their greatest common factor, i.e. GCF of 25 and 100.
⇒ Factors of 25 and 100:
- Factors of 25 = 1, 5, 25
- Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
Therefore, the GCF of 25 and 100 is 25.
Example 3: Find the GCF of 25 and 100, if their LCM is 100.

Solution:

∵ LCM × GCF = 25 × 100
⇒ GCF(25, 100) = (25 × 100)/100 = 25
Therefore, the greatest common factor of 25 and 100 is 25.

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FAQs on GCF of 25 and 100

What is the GCF of 25 and 100?

The GCF of 25 and 100 is 25. To calculate the GCF of 25 and 100, we need to factor each number (factors of 25 = 1, 5, 25; factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100) and choose the greatest factor that exactly divides both 25 and 100, i.e., 25.

How to Find the GCF of 25 and 100 by Prime Factorization?

To find the GCF of 25 and 100, we will find the prime factorization of the given numbers, i.e. 25 = 5 × 5; 100 = 2 × 2 × 5 × 5.
⇒ Since 5, 5 are common terms in the prime factorization of 25 and 100. Hence, GCF(25, 100) = 5 × 5 = 25
☛ What is a Prime Number?

What are the Methods to Find GCF of 25 and 100?

There are three commonly used methods to find the GCF of 25 and 100.

By Euclidean Algorithm
By Prime Factorization
By Long Division

What is the Relation Between LCM and GCF of 25, 100?

The following equation can be used to express the relation between LCM and GCF of 25 and 100, i.e. GCF × LCM = 25 × 100.

If the GCF of 100 and 25 is 25, Find its LCM.

GCF(100, 25) × LCM(100, 25) = 100 × 25
Since the GCF of 100 and 25 = 25
⇒ 25 × LCM(100, 25) = 2500
Therefore, LCM = 100
☛ Greatest Common Factor Calculator

How to Find the GCF of 25 and 100 by Long Division Method?

To find the GCF of 25, 100 using long division method, 100 is divided by 25. The corresponding divisor (25) when remainder equals 0 is taken as GCF.

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