GCF that 5 and also 10 is the largest feasible number the divides 5 and 10 specifically without any remainder. The determinants of 5 and 10 room 1, 5 and also 1, 2, 5, 10 respectively. There are 3 generally used techniques to uncover the GCF that 5 and also 10 - lengthy division, prime factorization, and Euclidean algorithm.

You are watching: What is the greatest common factor of 5 and 10

1.GCF the 5 and 10
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF that 5 and 10 is 5.

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Explanation:

The GCF of two non-zero integers, x(5) and y(10), is the best positive essence m(5) that divides both x(5) and y(10) without any kind of remainder.


Let's look at the different methods for finding the GCF the 5 and 10.

Using Euclid's AlgorithmLong department MethodPrime administrate Method

GCF that 5 and 10 by 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 = 10 and also Y = 5

GCF(10, 5) = GCF(5, 10 mod 5) = GCF(5, 0)GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, wherein X ≠ 0)

Therefore, the value of GCF that 5 and also 10 is 5.

GCF the 5 and 10 by lengthy Division

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GCF the 5 and 10 is the divisor the we gain when the remainder becomes 0 ~ doing long department repeatedly.

Step 2: due to the fact that the remainder = 0, the divisor (5) is the GCF that 5 and also 10.

The matching divisor (5) is the GCF the 5 and 10.

GCF of 5 and also 10 by prime Factorization

Prime factorization of 5 and also 10 is (5) and (2 × 5) respectively. As visible, 5 and 10 have only one usual prime variable i.e. 5. Hence, the GCF the 5 and also 10 is 5.

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GCF of 5 and also 10 Examples


Example 1: discover the GCF the 5 and 10, if their LCM is 10.

Solution:

∵ LCM × GCF = 5 × 10⇒ GCF(5, 10) = (5 × 10)/10 = 5Therefore, the greatest usual factor that 5 and also 10 is 5.


Example 2: The product of 2 numbers is 50. If their GCF is 5, what is your LCM?

Solution:

Given: GCF = 5 and also product of number = 50∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 50/5Therefore, the LCM is 10.


Example 3: find the biggest number the divides 5 and 10 exactly.

Solution:

The greatest number the divides 5 and also 10 specifically is your greatest typical factor, i.e. GCF of 5 and 10.⇒ components of 5 and 10:

Factors the 5 = 1, 5Factors the 10 = 1, 2, 5, 10

Therefore, the GCF of 5 and 10 is 5.


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FAQs top top GCF that 5 and 10

What is the GCF that 5 and 10?

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

What are the methods to discover GCF of 5 and 10?

There room three commonly used approaches to discover the GCF of 5 and also 10.

By long DivisionBy Listing common FactorsBy element Factorization

If the GCF that 10 and also 5 is 5, discover its LCM.

GCF(10, 5) × LCM(10, 5) = 10 × 5Since the GCF of 10 and also 5 = 5⇒ 5 × LCM(10, 5) = 50Therefore, LCM = 10☛ GCF Calculator

What is the Relation in between LCM and also GCF that 5, 10?

The complying with equation have the right to be used to refer the relation between Least usual Multiple and GCF the 5 and also 10, i.e. GCF × LCM = 5 × 10.

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How to uncover the GCF that 5 and 10 by element Factorization?

To uncover the GCF of 5 and 10, we will uncover the prime factorization of the provided numbers, i.e. 5 = 5; 10 = 2 × 5.⇒ since 5 is the only usual prime factor of 5 and also 10. Hence, GCF (5, 10) = 5.☛ element Numbers

How to find the GCF the 5 and also 10 by Long division Method?

To find the GCF of 5, 10 utilizing long department method, 10 is split by 5. The matching divisor (5) once remainder amounts to 0 is taken as GCF.