GCF that 3 and 6 is the largest feasible number that divides 3 and also 6 precisely without any type of remainder. The factors of 3 and also 6 space 1, 3 and 1, 2, 3, 6 respectively. There space 3 commonly used approaches to discover the GCF the 3 and 6 - element factorization, lengthy division, and also Euclidean algorithm.

You are watching: What is the greatest common factor of 3 and 6

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

Answer: GCF the 3 and also 6 is 3.

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Explanation:

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


The methods to uncover the GCF that 3 and also 6 are defined below.

Long department MethodPrime administrate MethodUsing Euclid's Algorithm

GCF of 3 and also 6 by lengthy Division

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GCF the 3 and 6 is the divisor that we acquire when the remainder becomes 0 after ~ doing long department repeatedly.

Step 2: because the remainder = 0, the divisor (3) is the GCF of 3 and also 6.

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

GCF the 3 and also 6 by element Factorization

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

GCF of 3 and also 6 by Euclidean Algorithm

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

Here X = 6 and also Y = 3

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

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

☛ also Check:


GCF of 3 and also 6 Examples


Example 1: The product of 2 numbers is 18. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 18∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 18/3Therefore, the LCM is 6.


Example 2: discover the GCF that 3 and also 6, if their LCM is 6.

Solution:

∵ LCM × GCF = 3 × 6⇒ GCF(3, 6) = (3 × 6)/6 = 3Therefore, the greatest typical factor the 3 and 6 is 3.


Example 3: For 2 numbers, GCF = 3 and also LCM = 6. If one number is 3, uncover the various other number.

Solution:

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


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FAQs ~ above GCF the 3 and 6

What is the GCF that 3 and 6?

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

If the GCF that 6 and 3 is 3, discover its LCM.

GCF(6, 3) × LCM(6, 3) = 6 × 3Since the GCF that 6 and also 3 = 3⇒ 3 × LCM(6, 3) = 18Therefore, LCM = 6☛ Greatest usual Factor Calculator

What space the methods to discover GCF of 3 and also 6?

There room three generally used methods to discover the GCF the 3 and also 6.

By Listing common FactorsBy lengthy DivisionBy element Factorization

How to find the GCF the 3 and also 6 by element Factorization?

To discover the GCF that 3 and 6, us will find the element factorization that the offered numbers, i.e. 3 = 3; 6 = 2 × 3.⇒ due to the fact that 3 is the only usual prime aspect of 3 and 6. Hence, GCF (3, 6) = 3.☛ prime Numbers

What is the Relation between LCM and GCF the 3, 6?

The adhering to equation have the right to be used to to express the relation in between LCM and GCF that 3 and also 6, i.e. GCF × LCM = 3 × 6.

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How to discover the GCF that 3 and also 6 by Long division Method?

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