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GCF of 2 and 8

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

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

What is GCF of 2 and 8?

Answer: GCF of 2 and 8 is 2.

Explanation:

The GCF of two non-zero integers, x(2) and y(8), is the greatest positive integer m(2) that divides both x(2) and y(8) without any remainder.

Methods to Find GCF of 2 and 8

The methods to find the GCF of 2 and 8 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 2 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 = 2

GCF(8, 2) = GCF(2, 8 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 2 and 8 is 2.

GCF of 2 and 8 by Long Division

GCF of 2 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 2 (smaller number).
Step 2: Since the remainder = 0, the divisor (2) is the GCF of 2 and 8.

The corresponding divisor (2) is the GCF of 2 and 8.

GCF of 2 and 8 by Listing Common Factors

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

There are 2 common factors of 2 and 8, that are 1 and 2. Therefore, the greatest common factor of 2 and 8 is 2.

☛ Also Check:

GCF of 2 and 8 Examples

Example 1: For two numbers, GCF = 2 and LCM = 8. If one number is 8, find the other number.

Solution:

Given: GCF (y, 8) = 2 and LCM (y, 8) = 8
∵ GCF × LCM = 8 × (y)
⇒ y = (GCF × LCM)/8
⇒ y = (2 × 8)/8
⇒ y = 2
Therefore, the other number is 2.
Example 2: Find the greatest number that divides 2 and 8 exactly.

Solution:

The greatest number that divides 2 and 8 exactly is their greatest common factor, i.e. GCF of 2 and 8.
⇒ Factors of 2 and 8:
- Factors of 2 = 1, 2
- Factors of 8 = 1, 2, 4, 8
Therefore, the GCF of 2 and 8 is 2.
Example 3: Find the GCF of 2 and 8, if their LCM is 8.

Solution:

∵ LCM × GCF = 2 × 8
⇒ GCF(2, 8) = (2 × 8)/8 = 2
Therefore, the greatest common factor of 2 and 8 is 2.

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FAQs on GCF of 2 and 8

What is the GCF of 2 and 8?

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

What are the Methods to Find GCF of 2 and 8?

There are three commonly used methods to find the GCF of 2 and 8.

By Long Division
By Listing Common Factors
By Prime Factorization

How to Find the GCF of 2 and 8 by Prime Factorization?

To find the GCF of 2 and 8, we will find the prime factorization of the given numbers, i.e. 2 = 2; 8 = 2 × 2 × 2.
⇒ Since 2 is the only common prime factor of 2 and 8. Hence, GCF (2, 8) = 2.
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 2, 8?

The following equation can be used to express the relation between LCM and GCF of 2 and 8, i.e. GCF × LCM = 2 × 8.

If the GCF of 8 and 2 is 2, Find its LCM.

GCF(8, 2) × LCM(8, 2) = 8 × 2
Since the GCF of 8 and 2 = 2
⇒ 2 × LCM(8, 2) = 16
Therefore, LCM = 8
☛ Greatest Common Factor Calculator

How to Find the GCF of 2 and 8 by Long Division Method?

To find the GCF of 2, 8 using long division method, 8 is divided by 2. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

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