GCF that 3 and 6 is the largest feasible number that divides 3 and 6 precisely without any remainder. The components of 3 and 6 room 1, 3 and 1, 2, 3, 6 respectively. There room 3 typically used techniques to find the GCF of 3 and also 6 - prime factorization, long division, and also Euclidean algorithm.

You are watching: Greatest common factor of 3 and 6

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

Answer: GCF of 3 and also 6 is 3.

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Explanation:

The GCF of 2 non-zero integers, x(3) and also y(6), is the best positive integer m(3) that divides both x(3) and also y(6) without any remainder.


The techniques to find the GCF of 3 and also 6 are described below.

Long division MethodPrime administrate MethodUsing Euclid's Algorithm

GCF of 3 and also 6 by lengthy Division

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

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

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

GCF that 3 and also 6 by element Factorization

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

GCF of 3 and 6 through Euclidean Algorithm

As per 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|, where X ≠ 0)

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

☛ also Check:


GCF the 3 and 6 Examples


Example 1: The product of 2 numbers is 18. If your GCF is 3, what is your 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: discover the GCF of 3 and also 6, if your LCM is 6.

Solution:

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


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


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FAQs top top GCF that 3 and also 6

What is the GCF of 3 and also 6?

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

If the GCF the 6 and also 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 room the approaches to discover GCF the 3 and also 6?

There room three commonly used approaches to uncover the GCF of 3 and 6.

By Listing typical FactorsBy long DivisionBy prime Factorization

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

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

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

The complying with equation deserve to be supplied to to express the relation between LCM and GCF that 3 and 6, i.e. GCF × LCM = 3 × 6.

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

To uncover the GCF that 3, 6 utilizing long department method, 6 is divided by 3. The equivalent divisor (3) as soon as remainder equates to 0 is taken together GCF.