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GCF of 4 and 6

GCF of 4 and 6 is the largest possible number that divides 4 and 6 exactly without any remainder. The factors of 4 and 6 are 1, 2, 4 and 1, 2, 3, 6 respectively. There are 3 commonly used methods to find the GCF of 4 and 6 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 4 and 6
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 4 and 6?

Answer: GCF of 4 and 6 is 2.

Explanation:

The GCF of two non-zero integers, x(4) and y(6), is the greatest positive integer m(2) that divides both x(4) and y(6) without any remainder.

Methods to Find GCF of 4 and 6

Let's look at the different methods for finding the GCF of 4 and 6.

Using Euclid's Algorithm
Prime Factorization Method
Listing Common Factors

GCF of 4 and 6 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 = 6 and Y = 4

GCF(6, 4) = GCF(4, 6 mod 4) = GCF(4, 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 4 and 6 is 2.

GCF of 4 and 6 by Prime Factorization

Prime factorization of 4 and 6 is (2 × 2) and (2 × 3) respectively. As visible, 4 and 6 have only one common prime factor i.e. 2. Hence, the GCF of 4 and 6 is 2.

GCF of 4 and 6 by Listing Common Factors

Factors of 4: 1, 2, 4
Factors of 6: 1, 2, 3, 6

There are 2 common factors of 4 and 6, that are 1 and 2. Therefore, the greatest common factor of 4 and 6 is 2.

☛ Also Check:

GCF of 4 and 6 Examples

Example 1: The product of two numbers is 24. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 24
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 24/2
Therefore, the LCM is 12.
Example 2: For two numbers, GCF = 2 and LCM = 12. If one number is 6, find the other number.

Solution:

Given: GCF (x, 6) = 2 and LCM (x, 6) = 12
∵ GCF × LCM = 6 × (x)
⇒ x = (GCF × LCM)/6
⇒ x = (2 × 12)/6
⇒ x = 4
Therefore, the other number is 4.
Example 3: Find the GCF of 4 and 6, if their LCM is 12.

Solution:

∵ LCM × GCF = 4 × 6
⇒ GCF(4, 6) = (4 × 6)/12 = 2
Therefore, the greatest common factor of 4 and 6 is 2.

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FAQs on GCF of 4 and 6

What is the GCF of 4 and 6?

The GCF of 4 and 6 is 2. To calculate the GCF of 4 and 6, we need to factor each number (factors of 4 = 1, 2, 4; factors of 6 = 1, 2, 3, 6) and choose the greatest factor that exactly divides both 4 and 6, i.e., 2.

What are the Methods to Find GCF of 4 and 6?

There are three commonly used methods to find the GCF of 4 and 6.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the GCF of 4 and 6 by Prime Factorization?

To find the GCF of 4 and 6, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 6 = 2 × 3.
⇒ Since 2 is the only common prime factor of 4 and 6. Hence, GCF (4, 6) = 2.
☛ What are Prime Numbers?

How to Find the GCF of 4 and 6 by Long Division Method?

To find the GCF of 4, 6 using long division method, 6 is divided by 4. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

If the GCF of 6 and 4 is 2, Find its LCM.

GCF(6, 4) × LCM(6, 4) = 6 × 4
Since the GCF of 6 and 4 = 2
⇒ 2 × LCM(6, 4) = 24
Therefore, LCM = 12
☛ GCF Calculator

What is the Relation Between LCM and GCF of 4, 6?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 4 and 6, i.e. GCF × LCM = 4 × 6.

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