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GCF of 25 and 55

GCF of 25 and 55 is the largest possible number that divides 25 and 55 exactly without any remainder. The factors of 25 and 55 are 1, 5, 25 and 1, 5, 11, 55 respectively. There are 3 commonly used methods to find the GCF of 25 and 55 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 25 and 55
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 25 and 55?

Answer: GCF of 25 and 55 is 5.

Explanation:

The GCF of two non-zero integers, x(25) and y(55), is the greatest positive integer m(5) that divides both x(25) and y(55) without any remainder.

Methods to Find GCF of 25 and 55

The methods to find the GCF of 25 and 55 are explained below.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 25 and 55 by Long Division

GCF of 25 and 55 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 55 (larger number) by 25 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (25) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 25 and 55.

GCF of 25 and 55 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 = 55 and Y = 25

GCF(55, 25) = GCF(25, 55 mod 25) = GCF(25, 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 25 and 55 is 5.

GCF of 25 and 55 by Listing Common Factors

Factors of 25: 1, 5, 25
Factors of 55: 1, 5, 11, 55

There are 2 common factors of 25 and 55, that are 1 and 5. Therefore, the greatest common factor of 25 and 55 is 5.

☛ Also Check:

GCF of 25 and 55 Examples

Example 1: Find the GCF of 25 and 55, if their LCM is 275.

Solution:

∵ LCM × GCF = 25 × 55
⇒ GCF(25, 55) = (25 × 55)/275 = 5
Therefore, the greatest common factor of 25 and 55 is 5.
Example 2: For two numbers, GCF = 5 and LCM = 275. If one number is 25, find the other number.

Solution:

Given: GCF (x, 25) = 5 and LCM (x, 25) = 275
∵ GCF × LCM = 25 × (x)
⇒ x = (GCF × LCM)/25
⇒ x = (5 × 275)/25
⇒ x = 55
Therefore, the other number is 55.
Example 3: Find the greatest number that divides 25 and 55 exactly.

Solution:

The greatest number that divides 25 and 55 exactly is their greatest common factor, i.e. GCF of 25 and 55.
⇒ Factors of 25 and 55:
- Factors of 25 = 1, 5, 25
- Factors of 55 = 1, 5, 11, 55
Therefore, the GCF of 25 and 55 is 5.

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FAQs on GCF of 25 and 55

What is the GCF of 25 and 55?

The GCF of 25 and 55 is 5. To calculate the greatest common factor of 25 and 55, we need to factor each number (factors of 25 = 1, 5, 25; factors of 55 = 1, 5, 11, 55) and choose the greatest factor that exactly divides both 25 and 55, i.e., 5.

How to Find the GCF of 25 and 55 by Prime Factorization?

To find the GCF of 25 and 55, we will find the prime factorization of the given numbers, i.e. 25 = 5 × 5; 55 = 5 × 11.
⇒ Since 5 is the only common prime factor of 25 and 55. Hence, GCF (25, 55) = 5.
☛ Prime Numbers

How to Find the GCF of 25 and 55 by Long Division Method?

To find the GCF of 25, 55 using long division method, 55 is divided by 25. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 25 and 55?

There are three commonly used methods to find the GCF of 25 and 55.

By Prime Factorization
By Euclidean Algorithm
By Long Division

If the GCF of 55 and 25 is 5, Find its LCM.

GCF(55, 25) × LCM(55, 25) = 55 × 25
Since the GCF of 55 and 25 = 5
⇒ 5 × LCM(55, 25) = 1375
Therefore, LCM = 275
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 25, 55?

The following equation can be used to express the relation between LCM and GCF of 25 and 55, i.e. GCF × LCM = 25 × 55.

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