GCF of 3 and also 6 is the largest feasible number the divides 3 and also 6 specifically without any remainder. The components of 3 and also 6 space 1, 3 and also 1, 2, 3, 6 respectively. There room 3 generally used methods to uncover the GCF of 3 and 6 - prime factorization, lengthy division, and Euclidean algorithm.

You are watching: What is the gcf of 3 and 6

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

Answer: GCF of 3 and also 6 is 3.

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Explanation:

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


The techniques to discover the GCF that 3 and 6 are explained below.

Long division MethodPrime administer MethodUsing Euclid's Algorithm

GCF the 3 and also 6 by lengthy Division

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GCF of 3 and also 6 is the divisor the we acquire when the remainder i do not care 0 ~ doing long department repeatedly.

Step 2: due to the fact that the remainder = 0, the divisor (3) is the GCF of 3 and 6.

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

GCF the 3 and also 6 by element Factorization

Prime factorization of 3 and also 6 is (3) and (2 × 3) respectively. Together visible, 3 and also 6 have actually only one common prime aspect i.e. 3. Hence, the GCF that 3 and also 6 is 3.

GCF the 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 mode 3) = GCF(3, 0)GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, whereby X ≠ 0)

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

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GCF that 3 and 6 Examples


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

Solution:

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


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


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FAQs ~ above GCF of 3 and 6

What is the GCF of 3 and 6?

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

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

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

What room the methods to find GCF that 3 and also 6?

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

By Listing usual FactorsBy long DivisionBy element Factorization

How to uncover the GCF that 3 and also 6 by prime Factorization?

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

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

The complying with equation have the right to be provided to refer the relation in between LCM and GCF of 3 and 6, i.e. GCF × LCM = 3 × 6.

See more: Iron (Iii) Oxide Chemical Formula, Iron(Ii,Iii) Oxide

How to find the GCF the 3 and also 6 through Long division Method?

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