GCF that 6 and 10 is the largest feasible number that divides 6 and 10 specifically without any kind of remainder. The factors of 6 and also 10 space 1, 2, 3, 6 and also 1, 2, 5, 10 respectively. There space 3 typically used techniques to discover the GCF the 6 and also 10 - element factorization, Euclidean algorithm, and also long division.

You are watching: Greatest common factor of 6 and 10

1.GCF of 6 and 10
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF the 6 and also 10 is 2.

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Explanation:

The GCF of two non-zero integers, x(6) and also y(10), is the best positive creature m(2) the divides both x(6) and y(10) without any kind of remainder.


The approaches to discover the GCF of 6 and 10 are described below.

Prime administrate MethodListing common FactorsUsing Euclid's Algorithm

GCF of 6 and also 10 by element Factorization

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Prime administrate of 6 and also 10 is (2 × 3) and also (2 × 5) respectively. As visible, 6 and 10 have only one typical prime aspect i.e. 2. Hence, the GCF of 6 and 10 is 2.

GCF of 6 and 10 through Listing typical Factors

Factors the 6: 1, 2, 3, 6Factors that 10: 1, 2, 5, 10

There space 2 usual factors that 6 and 10, that room 1 and also 2. Therefore, the greatest typical factor the 6 and 10 is 2.

GCF that 6 and also 10 by Euclidean Algorithm

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

Here X = 10 and Y = 6

GCF(10, 6) = GCF(6, 10 mode 6) = GCF(6, 4)GCF(6, 4) = GCF(4, 6 mode 4) = GCF(4, 2)GCF(4, 2) = GCF(2, 4 mode 2) = GCF(2, 0)GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the worth of GCF of 6 and also 10 is 2.

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GCF the 6 and also 10 Examples


Example 1: The product of 2 numbers is 60. If your GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and also product of number = 60∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 60/2Therefore, the LCM is 30.


Example 2: discover the best number the divides 6 and 10 exactly.

Solution:

The greatest number that divides 6 and 10 specifically is your greatest usual factor, i.e. GCF the 6 and 10.⇒ factors of 6 and 10:

Factors the 6 = 1, 2, 3, 6Factors that 10 = 1, 2, 5, 10

Therefore, the GCF of 6 and also 10 is 2.


Example 3: discover the GCF the 6 and also 10, if your LCM is 30.

Solution:

∵ LCM × GCF = 6 × 10⇒ GCF(6, 10) = (6 × 10)/30 = 2Therefore, the greatest typical factor the 6 and also 10 is 2.


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FAQs on GCF that 6 and 10

What is the GCF of 6 and also 10?

The GCF that 6 and also 10 is 2. To calculate the GCF of 6 and 10, we require to factor each number (factors that 6 = 1, 2, 3, 6; determinants of 10 = 1, 2, 5, 10) and choose the greatest aspect that precisely divides both 6 and 10, i.e., 2.

How to uncover the GCF the 6 and 10 by Long division Method?

To find the GCF of 6, 10 making use of long division method, 10 is divided by 6. The corresponding divisor (2) once remainder equals 0 is taken together GCF.

What are the methods to uncover GCF the 6 and also 10?

There space three commonly used techniques to discover the GCF of 6 and 10.

By long DivisionBy Euclidean AlgorithmBy element Factorization

How to uncover the GCF the 6 and also 10 by element Factorization?

To discover the GCF the 6 and also 10, we will uncover the element factorization the the offered numbers, i.e. 6 = 2 × 3; 10 = 2 × 5.⇒ since 2 is the only usual prime factor of 6 and 10. Hence, GCF (6, 10) = 2.☛ What space Prime Numbers?

If the GCF the 10 and also 6 is 2, find its LCM.

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GCF(10, 6) × LCM(10, 6) = 10 × 6Since the GCF that 10 and 6 = 2⇒ 2 × LCM(10, 6) = 60Therefore, LCM = 30☛ Greatest common Factor Calculator

What is the Relation in between LCM and also GCF that 6, 10?

The adhering to equation have the right to be supplied to refer the relation between LCM and GCF of 6 and also 10, i.e. GCF × LCM = 6 × 10.