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GCF of 8 and 25

GCF of 8 and 25 is the largest possible number that divides 8 and 25 exactly without any remainder. The factors of 8 and 25 are 1, 2, 4, 8 and 1, 5, 25 respectively. There are 3 commonly used methods to find the GCF of 8 and 25 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 8 and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 8 and 25?

Answer: GCF of 8 and 25 is 1.

Explanation:

The GCF of two non-zero integers, x(8) and y(25), is the greatest positive integer m(1) that divides both x(8) and y(25) without any remainder.

Methods to Find GCF of 8 and 25

Let's look at the different methods for finding the GCF of 8 and 25.

Listing Common Factors
Long Division Method
Using Euclid's Algorithm

GCF of 8 and 25 by Listing Common Factors

Factors of 8: 1, 2, 4, 8
Factors of 25: 1, 5, 25

Since, 1 is the only common factor between 8 and 25. The Greatest Common Factor of 8 and 25 is 1.

GCF of 8 and 25 by Long Division

GCF of 8 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 8 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (8) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 8 and 25.

GCF of 8 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 = 8

GCF(25, 8) = GCF(8, 25 mod 8) = GCF(8, 1)
GCF(8, 1) = GCF(1, 8 mod 1) = GCF(1, 0)
GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 8 and 25 is 1.

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GCF of 8 and 25 Examples

Example 1: The product of two numbers is 200. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 200
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 200/1
Therefore, the LCM is 200.
Example 2: Find the greatest number that divides 8 and 25 exactly.

Solution:

The greatest number that divides 8 and 25 exactly is their greatest common factor, i.e. GCF of 8 and 25.
⇒ Factors of 8 and 25:
- Factors of 8 = 1, 2, 4, 8
- Factors of 25 = 1, 5, 25
Therefore, the GCF of 8 and 25 is 1.
Example 3: For two numbers, GCF = 1 and LCM = 200. If one number is 25, find the other number.

Solution:

Given: GCF (y, 25) = 1 and LCM (y, 25) = 200
∵ GCF × LCM = 25 × (y)
⇒ y = (GCF × LCM)/25
⇒ y = (1 × 200)/25
⇒ y = 8
Therefore, the other number is 8.

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FAQs on GCF of 8 and 25

What is the GCF of 8 and 25?

The GCF of 8 and 25 is 1. To calculate the greatest common factor of 8 and 25, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 25 = 1, 5, 25) and choose the greatest factor that exactly divides both 8 and 25, i.e., 1.

How to Find the GCF of 8 and 25 by Prime Factorization?

To find the GCF of 8 and 25, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 25 = 5 × 5.
⇒ There is no common prime factor for 8 and 25. Hence, GCF (8, 25) = 1.
☛ What is a Prime Number?

What is the Relation Between LCM and GCF of 8, 25?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 8 and 25, i.e. GCF × LCM = 8 × 25.

If the GCF of 25 and 8 is 1, Find its LCM.

GCF(25, 8) × LCM(25, 8) = 25 × 8
Since the GCF of 25 and 8 = 1
⇒ 1 × LCM(25, 8) = 200
Therefore, LCM = 200
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How to Find the GCF of 8 and 25 by Long Division Method?

To find the GCF of 8, 25 using long division method, 25 is divided by 8. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 8 and 25?

There are three commonly used methods to find the GCF of 8 and 25.

By Euclidean Algorithm
By Prime Factorization
By Long Division

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