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

You are watching: What is the gcf of 5 and 10

1.GCF that 5 and also 10
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF that 5 and also 10 is 5.

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Explanation:

The GCF of two non-zero integers, x(5) and also y(10), is the greatest positive integer m(5) that divides both x(5) and y(10) without any type of remainder.


Let's look at the various methods because that finding the GCF of 5 and 10.

Using Euclid's AlgorithmLong division MethodPrime administrate Method

GCF of 5 and also 10 by Euclidean Algorithm

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

Here X = 10 and Y = 5

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

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

GCF that 5 and 10 by lengthy Division

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GCF that 5 and also 10 is the divisor the we obtain when the remainder becomes 0 after ~ doing long department repeatedly.

Step 2: because the remainder = 0, the divisor (5) is the GCF that 5 and 10.

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

GCF that 5 and also 10 by element Factorization

Prime factorization of 5 and also 10 is (5) and also (2 × 5) respectively. Together visible, 5 and 10 have actually only one typical prime aspect i.e. 5. Hence, the GCF the 5 and also 10 is 5.

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GCF the 5 and also 10 Examples


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

Solution:

∵ LCM × GCF = 5 × 10⇒ GCF(5, 10) = (5 × 10)/10 = 5Therefore, the greatest usual factor of 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 product of numbers = 50∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 50/5Therefore, the LCM is 10.


Example 3: uncover the best number the divides 5 and 10 exactly.

Solution:

The biggest number that divides 5 and also 10 specifically is your greatest common factor, i.e. GCF the 5 and 10.⇒ determinants of 5 and 10:

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

Therefore, the GCF that 5 and 10 is 5.


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FAQs on GCF of 5 and also 10

What is the GCF that 5 and 10?

The GCF of 5 and also 10 is 5. To calculate the greatest common factor that 5 and 10, we need to variable each number (factors of 5 = 1, 5; determinants of 10 = 1, 2, 5, 10) and also choose the greatest variable that exactly divides both 5 and 10, i.e., 5.

What are the approaches to find GCF that 5 and also 10?

There room three commonly used methods to uncover the GCF that 5 and 10.

By long DivisionBy Listing typical FactorsBy prime Factorization

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

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

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

The following equation deserve to be provided to to express the relation in between Least usual Multiple and also GCF of 5 and also 10, i.e. GCF × LCM = 5 × 10.

See more: " The Life You Save May Be Your Own Answers, The Life You Save May Be Your Own Flashcards

How to discover the GCF that 5 and also 10 by prime Factorization?

To find the GCF the 5 and also 10, us will find the element factorization that the offered numbers, i.e. 5 = 5; 10 = 2 × 5.⇒ because 5 is the only typical prime aspect of 5 and 10. Hence, GCF (5, 10) = 5.☛ prime Numbers

How to uncover the GCF of 5 and also 10 through Long department Method?

To uncover the GCF of 5, 10 utilizing long department method, 10 is separated by 5. The matching divisor (5) once remainder equals 0 is taken as GCF.