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GCF of 2 and 4

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

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

What is GCF of 2 and 4?

Answer: GCF of 2 and 4 is 2.

Explanation:

The GCF of two non-zero integers, x(2) and y(4), is the greatest positive integer m(2) that divides both x(2) and y(4) without any remainder.

Methods to Find GCF of 2 and 4

Let's look at the different methods for finding the GCF of 2 and 4.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

GCF of 2 and 4 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 = 4 and Y = 2

GCF(4, 2) = GCF(2, 4 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 2 and 4 is 2.

GCF of 2 and 4 by Listing Common Factors

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

There are 2 common factors of 2 and 4, that are 1 and 2. Therefore, the greatest common factor of 2 and 4 is 2.

GCF of 2 and 4 by Long Division

GCF of 2 and 4 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 4 (larger number) by 2 (smaller number).
Step 2: Since the remainder = 0, the divisor (2) is the GCF of 2 and 4.

The corresponding divisor (2) is the GCF of 2 and 4.

☛ Also Check:

GCF of 2 and 4 Examples

Example 1: The product of two numbers is 8. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 8
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 8/2
Therefore, the LCM is 4.
Example 2: Find the greatest number that divides 2 and 4 exactly.

Solution:

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

Solution:

∵ LCM × GCF = 2 × 4
⇒ GCF(2, 4) = (2 × 4)/4 = 2
Therefore, the greatest common factor of 2 and 4 is 2.

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FAQs on GCF of 2 and 4

What is the GCF of 2 and 4?

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

How to Find the GCF of 2 and 4 by Prime Factorization?

To find the GCF of 2 and 4, we will find the prime factorization of the given numbers, i.e. 2 = 2; 4 = 2 × 2.
⇒ Since 2 is the only common prime factor of 2 and 4. Hence, GCF (2, 4) = 2.
☛ Prime Numbers

What is the Relation Between LCM and GCF of 2, 4?

The following equation can be used to express the relation between Least Common Multiple and GCF of 2 and 4, i.e. GCF × LCM = 2 × 4.

How to Find the GCF of 2 and 4 by Long Division Method?

To find the GCF of 2, 4 using long division method, 4 is divided by 2. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 2 and 4?

There are three commonly used methods to find the GCF of 2 and 4.

By Long Division
By Euclidean Algorithm
By Prime Factorization

If the GCF of 4 and 2 is 2, Find its LCM.

GCF(4, 2) × LCM(4, 2) = 4 × 2
Since the GCF of 4 and 2 = 2
⇒ 2 × LCM(4, 2) = 8
Therefore, LCM = 4
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