GCF the 6 and 10 is the largest possible number that divides 6 and also 10 exactly without any type of remainder. The determinants of 6 and also 10 space 1, 2, 3, 6 and also 1, 2, 5, 10 respectively. There space 3 frequently used methods to find the GCF the 6 and 10 - prime factorization, Euclidean algorithm, and also long division.

You are watching: What is the gcf of 6 and 10

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

Answer: GCF the 6 and 10 is 2.

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Explanation:

The GCF of 2 non-zero integers, x(6) and also y(10), is the greatest positive essence m(2) that divides both x(6) and y(10) without any remainder.


The techniques to find the GCF the 6 and 10 are described below.

Prime administrate MethodListing typical FactorsUsing Euclid's Algorithm

GCF that 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 also 10 have actually only one typical prime variable i.e. 2. Hence, the GCF the 6 and also 10 is 2.

GCF that 6 and also 10 by Listing usual Factors

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

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

GCF of 6 and also 10 by Euclidean Algorithm

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

Here X = 10 and also Y = 6

GCF(10, 6) = GCF(6, 10 mod 6) = GCF(6, 4)GCF(6, 4) = GCF(4, 6 mod 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 that 6 and also 10 is 2.

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GCF of 6 and also 10 Examples


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

Solution:

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


Example 2: find the greatest number that divides 6 and 10 exactly.

Solution:

The best number that divides 6 and 10 specifically is your greatest typical 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 the 6 and 10 is 2.


Example 3: find the GCF of 6 and 10, if their LCM is 30.

Solution:

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


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FAQs on GCF of 6 and 10

What is the GCF the 6 and also 10?

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

How to uncover the GCF of 6 and also 10 by Long department Method?

To discover the GCF of 6, 10 making use of long division method, 10 is separated by 6. The equivalent divisor (2) when remainder equates to 0 is taken together GCF.

What space the techniques to discover GCF of 6 and also 10?

There are three commonly used methods to discover the GCF that 6 and also 10.

By long DivisionBy Euclidean AlgorithmBy element Factorization

How to find the GCF of 6 and also 10 by prime Factorization?

To uncover the GCF that 6 and also 10, we will uncover the prime factorization that the provided numbers, i.e. 6 = 2 × 3; 10 = 2 × 5.⇒ due to the fact that 2 is the only usual prime factor of 6 and 10. Hence, GCF (6, 10) = 2.☛ What room Prime Numbers?

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

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

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

The following equation deserve to be provided to refer the relation between LCM and also GCF of 6 and also 10, i.e. GCF × LCM = 6 × 10.