GCF that 4 and 6 is the largest possible number the divides 4 and 6 precisely without any remainder. The determinants of 4 and also 6 space 1, 2, 4 and 1, 2, 3, 6 respectively. There room 3 typically used methods to uncover the GCF of 4 and also 6 - long division, Euclidean algorithm, and prime factorization.

You are watching: What is the gcf of 4 and 6

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

Answer: GCF that 4 and also 6 is 2.

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Explanation:

The GCF of 2 non-zero integers, x(4) and y(6), is the best positive creature m(2) the divides both x(4) and also y(6) without any remainder.


Let's look in ~ the different methods for finding the GCF the 4 and 6.

Using Euclid's AlgorithmPrime administrate MethodListing common Factors

GCF the 4 and also 6 through 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 worth of GCF that 4 and 6 is 2.

GCF of 4 and 6 by prime Factorization

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

GCF the 4 and 6 through Listing typical Factors

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

There space 2 common factors that 4 and 6, that room 1 and also 2. Therefore, the greatest typical factor of 4 and also 6 is 2.

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GCF that 4 and also 6 Examples


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

Solution:

Given: GCF = 2 and also product of number = 24∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 24/2Therefore, the LCM is 12.


Example 2: For 2 numbers, GCF = 2 and LCM = 12. If one number is 6, find the various 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 = 4Therefore, the other number is 4.


Example 3: uncover the GCF that 4 and also 6, if your LCM is 12.

Solution:

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


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FAQs ~ above GCF of 4 and also 6

What is the GCF the 4 and also 6?

The GCF the 4 and also 6 is 2. To calculation the GCF the 4 and also 6, we need to element each number (factors the 4 = 1, 2, 4; factors of 6 = 1, 2, 3, 6) and also choose the greatest aspect that precisely divides both 4 and also 6, i.e., 2.

What space the approaches to uncover GCF that 4 and 6?

There space three commonly used techniques to find the GCF that 4 and 6.

By element FactorizationBy Euclidean AlgorithmBy long Division

How to discover the GCF of 4 and also 6 by prime Factorization?

To find the GCF of 4 and 6, we will find the element factorization of the given numbers, i.e. 4 = 2 × 2; 6 = 2 × 3.⇒ due to the fact that 2 is the only typical prime variable of 4 and 6. Hence, GCF (4, 6) = 2.☛ What are Prime Numbers?

How to discover the GCF of 4 and also 6 through Long department Method?

To discover the GCF that 4, 6 using long division method, 6 is split by 4. The matching divisor (2) once remainder amounts to 0 is taken as GCF.

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

See more: What Region South Of The Colorado River In Argentina ), Argentina: Land

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

What is the Relation in between LCM and also GCF of 4, 6?

The following equation have the right to be offered to to express the relation between LCM (Least typical Multiple) and also GCF of 4 and 6, i.e. GCF × LCM = 4 × 6.