GCF the 10 and also 20 is the largest possible number the divides 10 and also 20 specifically without any type of remainder. The components of 10 and also 20 room 1, 2, 5, 10 and also 1, 2, 4, 5, 10, 20 respectively. There space 3 generally used techniques to find the GCF of 10 and 20 - Euclidean algorithm, element factorization, and also long division.

You are watching: Greatest common factor of 10 and 20

1.GCF of 10 and also 20
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF of 10 and also 20 is 10.

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Explanation:

The GCF of two non-zero integers, x(10) and also y(20), is the greatest positive creature m(10) the divides both x(10) and y(20) without any kind of remainder.


Let's look in ~ the different methods because that finding the GCF of 10 and also 20.

Listing common FactorsLong division MethodUsing Euclid's Algorithm

GCF of 10 and also 20 by Listing common Factors

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Factors that 10: 1, 2, 5, 10Factors the 20: 1, 2, 4, 5, 10, 20

There space 4 common factors that 10 and 20, that are 1, 2, 10, and also 5. Therefore, the greatest typical factor that 10 and also 20 is 10.

GCF that 10 and also 20 by lengthy Division

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GCF that 10 and 20 is the divisor the we acquire when the remainder becomes 0 after doing long division repeatedly.

Step 2: since the remainder = 0, the divisor (10) is the GCF the 10 and 20.

The corresponding divisor (10) is the GCF of 10 and also 20.

GCF of 10 and also 20 by Euclidean Algorithm

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

Here X = 20 and also Y = 10

GCF(20, 10) = GCF(10, 20 mod 10) = GCF(10, 0)GCF(10, 0) = 10 (∵ GCF(X, 0) = |X|, wherein X ≠ 0)

Therefore, the worth of GCF that 10 and 20 is 10.

☛ also Check:


GCF of 10 and 20 Examples


Example 1: discover the biggest number the divides 10 and 20 exactly.

Solution:

The biggest number the divides 10 and also 20 precisely is their greatest typical factor, i.e. GCF the 10 and also 20.⇒ determinants of 10 and also 20:

Factors of 10 = 1, 2, 5, 10Factors of 20 = 1, 2, 4, 5, 10, 20

Therefore, the GCF that 10 and 20 is 10.


Example 2: The product of two numbers is 200. If their GCF is 10, what is your LCM?

Solution:

Given: GCF = 10 and also product of numbers = 200∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 200/10Therefore, the LCM is 20.


Example 3: uncover the GCF that 10 and also 20, if their LCM is 20.

Solution:

∵ LCM × GCF = 10 × 20⇒ GCF(10, 20) = (10 × 20)/20 = 10Therefore, the greatest common factor of 10 and 20 is 10.


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FAQs on GCF of 10 and also 20

What is the GCF that 10 and 20?

The GCF of 10 and 20 is 10. To calculation the greatest usual factor (GCF) of 10 and also 20, we need to variable each number (factors of 10 = 1, 2, 5, 10; factors of 20 = 1, 2, 4, 5, 10, 20) and also choose the greatest variable that specifically divides both 10 and also 20, i.e., 10.

How to discover the GCF that 10 and also 20 by prime Factorization?

To find the GCF that 10 and 20, us will find the element factorization that the offered numbers, i.e. 10 = 2 × 5; 20 = 2 × 2 × 5.⇒ because 2, 5 are common terms in the element factorization of 10 and 20. Hence, GCF(10, 20) = 2 × 5 = 10☛ What are Prime Numbers?

If the GCF that 20 and 10 is 10, uncover its LCM.

GCF(20, 10) × LCM(20, 10) = 20 × 10Since the GCF the 20 and also 10 = 10⇒ 10 × LCM(20, 10) = 200Therefore, LCM = 20☛ GCF Calculator

What is the Relation in between LCM and GCF that 10, 20?

The following equation deserve to be supplied to to express the relation between Least typical Multiple and GCF that 10 and also 20, i.e. GCF × LCM = 10 × 20.

How to uncover the GCF of 10 and 20 by Long division Method?

To uncover the GCF the 10, 20 using long division method, 20 is separated by 10. The corresponding divisor (10) when remainder equals 0 is taken together GCF.

See more: What Is 1.27 Repeating As A Fraction, View Question

What are the approaches to discover GCF that 10 and 20?

There space three generally used methods to uncover the GCF the 10 and 20.