GCF the 39 and also 6 is the largest feasible number that divides 39 and 6 precisely without any type of remainder. The determinants of 39 and also 6 are 1, 3, 13, 39 and also 1, 2, 3, 6 respectively. There are 3 generally used approaches to find the GCF that 39 and also 6 - long division, Euclidean algorithm, and also prime factorization.

You are watching: What is the gcf of 39 and 6

1.GCF the 39 and also 6
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF the 39 and 6 is 3.

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Explanation:

The GCF of 2 non-zero integers, x(39) and y(6), is the best positive creature m(3) the divides both x(39) and also y(6) without any remainder.


Let's look in ~ the different methods for finding the GCF the 39 and also 6.

Listing usual FactorsUsing Euclid's AlgorithmPrime factorization Method

GCF the 39 and also 6 by Listing typical Factors

Factors the 39: 1, 3, 13, 39Factors that 6: 1, 2, 3, 6

There space 2 common factors the 39 and 6, that space 1 and 3. Therefore, the greatest common factor of 39 and 6 is 3.

GCF of 39 and 6 by Euclidean Algorithm

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

Here X = 39 and Y = 6

GCF(39, 6) = GCF(6, 39 mode 6) = GCF(6, 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 worth of GCF the 39 and also 6 is 3.

GCF that 39 and 6 by element Factorization

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Prime administer of 39 and also 6 is (3 × 13) and also (2 × 3) respectively. Together visible, 39 and also 6 have actually only one common prime factor i.e. 3. Hence, the GCF that 39 and 6 is 3.

☛ also Check:


GCF that 39 and also 6 Examples


Example 1: find the GCF that 39 and also 6, if their LCM is 78.

Solution:

∵ LCM × GCF = 39 × 6⇒ GCF(39, 6) = (39 × 6)/78 = 3Therefore, the greatest common factor that 39 and also 6 is 3.


Example 2: For 2 numbers, GCF = 3 and LCM = 78. If one number is 6, uncover the other number.

Solution:

Given: GCF (x, 6) = 3 and also LCM (x, 6) = 78∵ GCF × LCM = 6 × (x)⇒ x = (GCF × LCM)/6⇒ x = (3 × 78)/6⇒ x = 39Therefore, the various other number is 39.


Example 3: The product of 2 numbers is 234. If your GCF is 3, what is your LCM?

Solution:

Given: GCF = 3 and product of number = 234∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 234/3Therefore, the LCM is 78.


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FAQs ~ above GCF that 39 and also 6

What is the GCF the 39 and 6?

The GCF that 39 and 6 is 3. To calculation the GCF (Greatest typical Factor) the 39 and 6, we need to aspect each number (factors that 39 = 1, 3, 13, 39; factors of 6 = 1, 2, 3, 6) and also choose the greatest variable that precisely divides both 39 and 6, i.e., 3.

How to discover the GCF the 39 and 6 by prime Factorization?

To uncover the GCF of 39 and 6, we will find the element factorization of the offered numbers, i.e. 39 = 3 × 13; 6 = 2 × 3.⇒ since 3 is the only usual prime element of 39 and 6. Hence, GCF (39, 6) = 3.☛ element Numbers

How to discover the GCF of 39 and also 6 through Long department Method?

To find the GCF the 39, 6 using long division method, 39 is split by 6. The corresponding divisor (3) when remainder equals 0 is taken together GCF.

What is the Relation between LCM and also GCF that 39, 6?

The adhering to equation can be supplied to refer the relation in between Least typical Multiple (LCM) and also GCF that 39 and 6, i.e. GCF × LCM = 39 × 6.

What space the methods to uncover GCF that 39 and 6?

There space three frequently used methods to discover the GCF that 39 and 6.

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By long DivisionBy element FactorizationBy Listing usual Factors

If the GCF the 6 and 39 is 3, uncover its LCM.

GCF(6, 39) × LCM(6, 39) = 6 × 39Since the GCF that 6 and 39 = 3⇒ 3 × LCM(6, 39) = 234Therefore, LCM = 78☛ Greatest common Factor Calculator