GCF of 4 and also 12 is the largest possible number that divides 4 and also 12 precisely without any type of remainder. The components of 4 and also 12 are 1, 2, 4 and 1, 2, 3, 4, 6, 12 respectively. There are 3 typically provided techniques to find the GCF of 4 and also 12 - long department, Euclidean algorithm, and also prime factorization.

You are watching: Greatest common factor of 4 and 12

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

Answer: GCF of 4 and 12 is 4.

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Explanation:

The GCF of 2 non-zero integers, x(4) and y(12), is the biggest positive integer m(4) that divides both x(4) and also y(12) without any kind of remainder.


The approaches to find the GCF of 4 and also 12 are explained listed below.

Long Division MethodPrime Factorization MethodUsing Euclid's Algorithm

GCF of 4 and also 12 by Long Division

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GCF of 4 and 12 is the divisor that we gain when the remainder becomes 0 after doing long division consistently.

Tip 2: Because the remainder = 0, the divisor (4) is the GCF of 4 and also 12.

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

GCF of 4 and 12 by Prime Factorization

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Prime factorization of 4 and 12 is (2 × 2) and also (2 × 2 × 3) respectively. As visible, 4 and 12 have widespread prime components. Hence, the GCF of 4 and 12 is 2 × 2 = 4.

GCF of 4 and also 12 by Euclidean Algorithm

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

Here X = 12 and also Y = 4

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

Because of this, the worth of GCF of 4 and 12 is 4.

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GCF of 4 and 12 Examples


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

Solution:

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

Factors of 4 = 1, 2, 4Factors of 12 = 1, 2, 3, 4, 6, 12

Because of this, the GCF of 4 and 12 is 4.


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

Solution:

Given: GCF (z, 12) = 4 and also 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 2 numbers is 48. If their GCF is 4, what is their LCM?

Solution:

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


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FAQs on GCF of 4 and 12

What is the GCF of 4 and also 12?

The GCF of 4 and also 12 is 4. To calculate the GCF of 4 and 12, we have to variable each number (determinants of 4 = 1, 2, 4; determinants of 12 = 1, 2, 3, 4, 6, 12) and select the best variable that precisely divides both 4 and also 12, i.e., 4.

What is the Relation Between LCM and GCF of 4, 12?

The complying with equation deserve to be supplied to expush the relation between LCM and also GCF of 4 and also 12, i.e. GCF × LCM = 4 × 12.

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

GCF(12, 4) × LCM(12, 4) = 12 × 4Due to the fact that the GCF of 12 and also 4 = 4⇒ 4 × LCM(12, 4) = 48Because of this, LCM = 12☛ GCF Calculator

How to Find the GCF of 4 and 12 by Prime Factorization?

To discover the GCF of 4 and also 12, we will uncover the prime factorization of the given numbers, i.e. 4 = 2 × 2; 12 = 2 × 2 × 3.⇒ Because 2, 2 are widespread terms in the prime factorization of 4 and also 12. Hence, GCF(4, 12) = 2 × 2 = 4☛ Prime Number

How to Find the GCF of 4 and also 12 by Long Division Method?

To uncover the GCF of 4, 12 utilizing long department method, 12 is split by 4. The corresponding divisor (4) when remainder equates to 0 is taken as GCF.

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What are the Methods to Find GCF of 4 and 12?

There are 3 typically supplied approaches to discover the GCF of 4 and also 12.