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GCF of 20 and 25

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

1.	GCF of 20 and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 20 and 25?

Answer: GCF of 20 and 25 is 5.

Explanation:

The GCF of two non-zero integers, x(20) and y(25), is the greatest positive integer m(5) that divides both x(20) and y(25) without any remainder.

Methods to Find GCF of 20 and 25

Let's look at the different methods for finding the GCF of 20 and 25.

Prime Factorization Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 20 and 25 by Prime Factorization

Prime factorization of 20 and 25 is (2 × 2 × 5) and (5 × 5) respectively. As visible, 20 and 25 have only one common prime factor i.e. 5. Hence, the GCF of 20 and 25 is 5.

GCF of 20 and 25 by Listing Common Factors

Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 25: 1, 5, 25

There are 2 common factors of 20 and 25, that are 1 and 5. Therefore, the greatest common factor of 20 and 25 is 5.

GCF of 20 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 = 20

GCF(25, 20) = GCF(20, 25 mod 20) = GCF(20, 5)
GCF(20, 5) = GCF(5, 20 mod 5) = GCF(5, 0)
GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 20 and 25 is 5.

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GCF of 20 and 25 Examples

Example 1: For two numbers, GCF = 5 and LCM = 100. If one number is 20, find the other number.

Solution:

Given: GCF (x, 20) = 5 and LCM (x, 20) = 100
∵ GCF × LCM = 20 × (x)
⇒ x = (GCF × LCM)/20
⇒ x = (5 × 100)/20
⇒ x = 25
Therefore, the other number is 25.
Example 2: The product of two numbers is 500. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 500
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 500/5
Therefore, the LCM is 100.
Example 3: Find the greatest number that divides 20 and 25 exactly.

Solution:

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

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FAQs on GCF of 20 and 25

What is the GCF of 20 and 25?

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

If the GCF of 25 and 20 is 5, Find its LCM.

GCF(25, 20) × LCM(25, 20) = 25 × 20
Since the GCF of 25 and 20 = 5
⇒ 5 × LCM(25, 20) = 500
Therefore, LCM = 100
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What are the Methods to Find GCF of 20 and 25?

There are three commonly used methods to find the GCF of 20 and 25.

By Prime Factorization
By Euclidean Algorithm
By Long Division

What is the Relation Between LCM and GCF of 20, 25?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 20 and 25, i.e. GCF × LCM = 20 × 25.

How to Find the GCF of 20 and 25 by Long Division Method?

To find the GCF of 20, 25 using long division method, 25 is divided by 20. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

How to Find the GCF of 20 and 25 by Prime Factorization?

To find the GCF of 20 and 25, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 25 = 5 × 5.
⇒ Since 5 is the only common prime factor of 20 and 25. Hence, GCF (20, 25) = 5.
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