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GCF of 5 and 8

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

1.	GCF of 5 and 8
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 5 and 8?

Answer: GCF of 5 and 8 is 1.

Explanation:

The GCF of two non-zero integers, x(5) and y(8), is the greatest positive integer m(1) that divides both x(5) and y(8) without any remainder.

Methods to Find GCF of 5 and 8

Let's look at the different methods for finding the GCF of 5 and 8.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

GCF of 5 and 8 by Listing Common Factors

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

Since, 1 is the only common factor between 5 and 8. The Greatest Common Factor of 5 and 8 is 1.

GCF of 5 and 8 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 = 8 and Y = 5

GCF(8, 5) = GCF(5, 8 mod 5) = GCF(5, 3)
GCF(5, 3) = GCF(3, 5 mod 3) = GCF(3, 2)
GCF(3, 2) = GCF(2, 3 mod 2) = GCF(2, 1)
GCF(2, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 5 and 8 is 1.

GCF of 5 and 8 by Long Division

GCF of 5 and 8 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 8 (larger number) by 5 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (5) by the remainder (3).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 5 and 8.

☛ Also Check:

GCF of 5 and 8 Examples

Example 1: For two numbers, GCF = 1 and LCM = 40. If one number is 8, find the other number.

Solution:

Given: GCF (z, 8) = 1 and LCM (z, 8) = 40
∵ GCF × LCM = 8 × (z)
⇒ z = (GCF × LCM)/8
⇒ z = (1 × 40)/8
⇒ z = 5
Therefore, the other number is 5.
Example 2: Find the GCF of 5 and 8, if their LCM is 40.

Solution:

∵ LCM × GCF = 5 × 8
⇒ GCF(5, 8) = (5 × 8)/40 = 1
Therefore, the greatest common factor of 5 and 8 is 1.
Example 3: Find the greatest number that divides 5 and 8 exactly.

Solution:

The greatest number that divides 5 and 8 exactly is their greatest common factor, i.e. GCF of 5 and 8.
⇒ Factors of 5 and 8:
- Factors of 5 = 1, 5
- Factors of 8 = 1, 2, 4, 8
Therefore, the GCF of 5 and 8 is 1.

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FAQs on GCF of 5 and 8

What is the GCF of 5 and 8?

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

What is the Relation Between LCM and GCF of 5, 8?

The following equation can be used to express the relation between LCM and GCF of 5 and 8, i.e. GCF × LCM = 5 × 8.

If the GCF of 8 and 5 is 1, Find its LCM.

GCF(8, 5) × LCM(8, 5) = 8 × 5
Since the GCF of 8 and 5 = 1
⇒ 1 × LCM(8, 5) = 40
Therefore, LCM = 40
☛ GCF Calculator

How to Find the GCF of 5 and 8 by Prime Factorization?

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

How to Find the GCF of 5 and 8 by Long Division Method?

To find the GCF of 5, 8 using long division method, 8 is divided by 5. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 5 and 8?

There are three commonly used methods to find the GCF of 5 and 8.

By Prime Factorization
By Long Division
By Euclidean Algorithm

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