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GCF of 4 and 12

GCF of 4 and 12 is the largest possible number that divides 4 and 12 exactly without any remainder. The factors of 4 and 12 are 1, 2, 4 and 1, 2, 3, 4, 6, 12 respectively. There are 3 commonly used methods to find the GCF of 4 and 12 - long division, Euclidean algorithm, and prime factorization.

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

What is GCF of 4 and 12?

Answer: GCF of 4 and 12 is 4.

Explanation:

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

Methods to Find GCF of 4 and 12

The methods to find the GCF of 4 and 12 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 4 and 12 by Long Division

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

Step 1: Divide 12 (larger number) by 4 (smaller number).
Step 2: Since the remainder = 0, the divisor (4) is the GCF of 4 and 12.

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

GCF of 4 and 12 by Prime Factorization

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

GCF of 4 and 12 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 = 12 and Y = 4

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

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

☛ Also Check:

GCF of 4 and 12 Examples

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

Solution:

The greatest number that divides 4 and 12 exactly is their greatest common factor, i.e. GCF of 4 and 12.
⇒ Factors of 4 and 12:
- Factors of 4 = 1, 2, 4
- Factors of 12 = 1, 2, 3, 4, 6, 12
Therefore, the GCF of 4 and 12 is 4.
Example 2: For two numbers, GCF = 4 and LCM = 12. If one number is 12, find 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 = 4
Therefore, the other number is 4.
Example 3: The product of two numbers is 48. If their GCF is 4, what is their LCM?

Solution:

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

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FAQs on GCF of 4 and 12

What is the GCF of 4 and 12?

The GCF of 4 and 12 is 4. To calculate the GCF of 4 and 12, we need to factor each number (factors of 4 = 1, 2, 4; factors of 12 = 1, 2, 3, 4, 6, 12) and choose the greatest factor that exactly divides both 4 and 12, i.e., 4.

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

The following equation can be used to express the relation between LCM and GCF of 4 and 12, i.e. GCF × LCM = 4 × 12.

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

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

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

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

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

To find the GCF of 4, 12 using long division method, 12 is divided by 4. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

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

There are three commonly used methods to find the GCF of 4 and 12.

By Prime Factorization
By Long Division
By Euclidean Algorithm

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