GCF that 4 and 12 is the largest feasible number that divides 4 and also 12 exactly without any remainder. The components of 4 and 12 room 1, 2, 4 and 1, 2, 3, 4, 6, 12 respectively. There space 3 frequently used approaches to find the GCF of 4 and also 12 - lengthy division, Euclidean algorithm, and also prime factorization.

You are watching: Greatest common factor of 4 and 12

1.GCF the 4 and 12
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF the 4 and 12 is 4.

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Explanation:

The GCF of two non-zero integers, x(4) and y(12), is the greatest positive essence m(4) that divides both x(4) and y(12) without any type of remainder.


The techniques to discover the GCF that 4 and 12 are explained below.

Long department MethodPrime administer MethodUsing Euclid's Algorithm

GCF that 4 and 12 by lengthy Division

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GCF that 4 and also 12 is the divisor that we get when the remainder becomes 0 after doing long department repeatedly.

Step 2: due to the fact that the remainder = 0, the divisor (4) is the GCF that 4 and 12.

The equivalent divisor (4) is the GCF the 4 and also 12.

GCF that 4 and also 12 by element Factorization

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Prime factorization of 4 and also 12 is (2 × 2) and (2 × 2 × 3) respectively. Together visible, 4 and also 12 have usual prime factors. Hence, the GCF of 4 and 12 is 2 × 2 = 4.

GCF that 4 and also 12 through Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mode Y)where X > Y and mod is the modulo operator.

Here X = 12 and Y = 4

GCF(12, 4) = GCF(4, 12 mode 4) = GCF(4, 0)GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 4 and also 12 is 4.

☛ additionally Check:


GCF the 4 and 12 Examples


Example 1: discover the best number that divides 4 and 12 exactly.

Solution:

The biggest number that divides 4 and also 12 exactly is their greatest typical factor, i.e. GCF that 4 and 12.⇒ components of 4 and also 12:

Factors the 4 = 1, 2, 4Factors that 12 = 1, 2, 3, 4, 6, 12

Therefore, the GCF that 4 and 12 is 4.


Example 2: For two numbers, GCF = 4 and LCM = 12. If one number is 12, uncover the other number.

Solution:

Given: GCF (z, 12) = 4 and LCM (z, 12) = 12∵ GCF × LCM = 12 × (z)⇒ z = (GCF × LCM)/12⇒ z = (4 × 12)/12⇒ z = 4Therefore, the other number is 4.


Example 3: The product of two numbers is 48. If your GCF is 4, what is your LCM?

Solution:

Given: GCF = 4 and also product of numbers = 48∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 48/4Therefore, the LCM is 12.


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FAQs top top GCF of 4 and also 12

What is the GCF of 4 and 12?

The GCF the 4 and also 12 is 4. To calculate the GCF of 4 and also 12, we require to variable each number (factors that 4 = 1, 2, 4; components of 12 = 1, 2, 3, 4, 6, 12) and choose the greatest aspect that precisely divides both 4 and 12, i.e., 4.

What is the Relation between LCM and GCF the 4, 12?

The complying with equation have the right to be provided to express the relation between LCM and GCF the 4 and also 12, i.e. GCF × LCM = 4 × 12.

If the GCF the 12 and also 4 is 4, discover its LCM.

GCF(12, 4) × LCM(12, 4) = 12 × 4Since the GCF that 12 and also 4 = 4⇒ 4 × LCM(12, 4) = 48Therefore, LCM = 12☛ GCF Calculator

How to find the GCF the 4 and also 12 by prime Factorization?

To uncover the GCF the 4 and 12, us will find the element factorization of the given numbers, i.e. 4 = 2 × 2; 12 = 2 × 2 × 3.⇒ due to the fact that 2, 2 are common terms in the element factorization the 4 and also 12. Hence, GCF(4, 12) = 2 × 2 = 4☛ prime Number

How to uncover the GCF of 4 and also 12 by Long department Method?

To find the GCF of 4, 12 making use of long department method, 12 is split by 4. The equivalent divisor (4) once remainder equals 0 is taken together GCF.

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What are the techniques to discover GCF of 4 and also 12?

There space three commonly used techniques to discover the GCF that 4 and also 12.