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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 nonzero 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.
☛ Also Check:
 GCF of 25 and 40 = 5
 GCF of 50 and 60 = 10
 GCF of 64 and 96 = 32
 GCF of 35 and 42 = 7
 GCF of 8 and 24 = 8
 GCF of 48 and 120 = 24
 GCF of 18 and 32 = 2
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.
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
☛ GCF Calculator
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.
☛ Prime Numbers
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