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GCF of 5 and 25

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

1.	GCF of 5 and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 5 and 25?

Answer: GCF of 5 and 25 is 5.

Explanation:

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

Methods to Find GCF of 5 and 25

The methods to find the GCF of 5 and 25 are explained below.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

GCF of 5 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 = 5

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

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

GCF of 5 and 25 by Prime Factorization

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

GCF of 5 and 25 by Long Division

GCF of 5 and 25 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 25 (larger number) by 5 (smaller number).
Step 2: Since the remainder = 0, the divisor (5) is the GCF of 5 and 25.

The corresponding divisor (5) is the GCF of 5 and 25.

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GCF of 5 and 25 Examples

Example 1: The product of two numbers is 125. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 125
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 125/5
Therefore, the LCM is 25.
Example 2: Find the greatest number that divides 5 and 25 exactly.

Solution:

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

Solution:

∵ LCM × GCF = 5 × 25
⇒ GCF(5, 25) = (5 × 25)/25 = 5
Therefore, the greatest common factor of 5 and 25 is 5.

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FAQs on GCF of 5 and 25

What is the GCF of 5 and 25?

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

What are the Methods to Find GCF of 5 and 25?

There are three commonly used methods to find the GCF of 5 and 25.

By Prime Factorization
By Listing Common Factors
By Long Division

What is the Relation Between LCM and GCF of 5, 25?

The following equation can be used to express the relation between LCM and GCF of 5 and 25, i.e. GCF × LCM = 5 × 25.

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

GCF(25, 5) × LCM(25, 5) = 25 × 5
Since the GCF of 25 and 5 = 5
⇒ 5 × LCM(25, 5) = 125
Therefore, LCM = 25
☛ Greatest Common Factor Calculator

How to Find the GCF of 5 and 25 by Prime Factorization?

To find the GCF of 5 and 25, we will find the prime factorization of the given numbers, i.e. 5 = 5; 25 = 5 × 5.
⇒ Since 5 is the only common prime factor of 5 and 25. Hence, GCF (5, 25) = 5.
☛ What are Prime Numbers?

How to Find the GCF of 5 and 25 by Long Division Method?

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

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