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GCF of 3 and 6

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

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

What is GCF of 3 and 6?

Answer: GCF of 3 and 6 is 3.

Explanation:

The GCF of two non-zero integers, x(3) and y(6), is the greatest positive integer m(3) that divides both x(3) and y(6) without any remainder.

Methods to Find GCF of 3 and 6

The methods to find the GCF of 3 and 6 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 3 and 6 by Long Division

GCF of 3 and 6 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 6 (larger number) by 3 (smaller number).
Step 2: Since the remainder = 0, the divisor (3) is the GCF of 3 and 6.

The corresponding divisor (3) is the GCF of 3 and 6.

GCF of 3 and 6 by Prime Factorization

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

GCF of 3 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 = 3

GCF(6, 3) = GCF(3, 6 mod 3) = GCF(3, 0)
GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 3 and 6 is 3.

☛ Also Check:

GCF of 3 and 6 Examples

Example 1: The product of two numbers is 18. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 18
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 18/3
Therefore, the LCM is 6.
Example 2: Find the GCF of 3 and 6, if their LCM is 6.

Solution:

∵ LCM × GCF = 3 × 6
⇒ GCF(3, 6) = (3 × 6)/6 = 3
Therefore, the greatest common factor of 3 and 6 is 3.
Example 3: For two numbers, GCF = 3 and LCM = 6. If one number is 3, find the other number.

Solution:

Given: GCF (y, 3) = 3 and LCM (y, 3) = 6
∵ GCF × LCM = 3 × (y)
⇒ y = (GCF × LCM)/3
⇒ y = (3 × 6)/3
⇒ y = 6
Therefore, the other number is 6.

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FAQs on GCF of 3 and 6

What is the GCF of 3 and 6?

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

If the GCF of 6 and 3 is 3, Find its LCM.

GCF(6, 3) × LCM(6, 3) = 6 × 3
Since the GCF of 6 and 3 = 3
⇒ 3 × LCM(6, 3) = 18
Therefore, LCM = 6
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 3 and 6?

There are three commonly used methods to find the GCF of 3 and 6.

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the GCF of 3 and 6 by Prime Factorization?

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

What is the Relation Between LCM and GCF of 3, 6?

The following equation can be used to express the relation between LCM and GCF of 3 and 6, i.e. GCF × LCM = 3 × 6.

How to Find the GCF of 3 and 6 by Long Division Method?

To find the GCF of 3, 6 using long division method, 6 is divided by 3. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

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