GCF the 3 and 6 is the largest possible number that divides 3 and 6 exactly without any type of remainder. The components of 3 and 6 are 1, 3 and also 1, 2, 3, 6 respectively. There room 3 frequently used techniques to uncover the GCF the 3 and 6 - element factorization, long division, and also Euclidean algorithm.

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

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

Answer: GCF that 3 and 6 is 3.

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Explanation:

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


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

Long department MethodPrime administer MethodUsing Euclid's Algorithm

GCF the 3 and also 6 by long Division

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GCF the 3 and also 6 is the divisor that we obtain when the remainder i do not care 0 ~ doing long division repeatedly.

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

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

GCF that 3 and 6 by prime Factorization

Prime administrate of 3 and also 6 is (3) and also (2 × 3) respectively. As visible, 3 and 6 have only one usual prime aspect i.e. 3. Hence, the GCF that 3 and 6 is 3.

GCF of 3 and 6 through Euclidean Algorithm

As every the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mode Y)where X > Y and also 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|, wherein X ≠ 0)

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

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GCF the 3 and also 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 the numbers⇒ LCM = Product/GCF = 18/3Therefore, the LCM is 6.


Example 2: uncover 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 of 3 and 6 is 3.


Example 3: For 2 numbers, GCF = 3 and also LCM = 6. If one number is 3, discover the 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 top top GCF of 3 and also 6

What is the GCF of 3 and also 6?

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

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

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

What room the methods to discover GCF that 3 and 6?

There are three typically used approaches to uncover the GCF the 3 and 6.

By Listing usual FactorsBy long DivisionBy prime Factorization

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

To find the GCF the 3 and also 6, we will uncover the prime factorization of the offered numbers, i.e. 3 = 3; 6 = 2 × 3.⇒ because 3 is the only usual prime variable of 3 and also 6. Hence, GCF (3, 6) = 3.☛ element Numbers

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

The following equation have the right to be supplied to refer the relation in between LCM and also GCF of 3 and also 6, i.e. GCF × LCM = 3 × 6.

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

To uncover the GCF of 3, 6 utilizing long division method, 6 is divided by 3. The matching divisor (3) when remainder equates to 0 is taken together GCF.