GCF the 20 and 40 is the largest feasible number that divides 20 and 40 exactly without any kind of remainder. The factors of 20 and also 40 room 1, 2, 4, 5, 10, 20 and also 1, 2, 4, 5, 8, 10, 20, 40 respectively. There are 3 commonly used approaches to discover the GCF the 20 and 40 - prime factorization, lengthy division, and Euclidean algorithm.

You are watching: Greatest common factor of 20 and 40

1.GCF the 20 and 40
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF the 20 and 40 is 20.

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Explanation:

The GCF of two non-zero integers, x(20) and also y(40), is the greatest positive integer m(20) the divides both x(20) and also y(40) without any kind of remainder.


Let's look at the different methods because that finding the GCF of 20 and 40.

Using Euclid's AlgorithmPrime administrate MethodLong division Method

GCF of 20 and 40 through Euclidean Algorithm

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

Here X = 40 and also Y = 20

GCF(40, 20) = GCF(20, 40 mode 20) = GCF(20, 0)GCF(20, 0) = 20 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the worth of GCF that 20 and 40 is 20.

GCF of 20 and 40 by element Factorization

Prime administer of 20 and 40 is (2 × 2 × 5) and (2 × 2 × 2 × 5) respectively. As visible, 20 and 40 have typical prime factors. Hence, the GCF of 20 and also 40 is 2 × 2 × 5 = 20.

GCF the 20 and 40 by lengthy Division

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GCF the 20 and also 40 is the divisor that we get when the remainder i do not care 0 ~ doing long department repeatedly.

Step 2: because the remainder = 0, the divisor (20) is the GCF of 20 and 40.

The corresponding divisor (20) is the GCF that 20 and also 40.

☛ also Check:


GCF of 20 and 40 Examples


Example 1: find the best number the divides 20 and also 40 exactly.

Solution:

The best number the divides 20 and also 40 exactly is your greatest usual factor, i.e. GCF the 20 and 40.⇒ determinants of 20 and also 40:

Factors that 20 = 1, 2, 4, 5, 10, 20Factors the 40 = 1, 2, 4, 5, 8, 10, 20, 40

Therefore, the GCF the 20 and 40 is 20.


Example 2: find the GCF of 20 and 40, if their LCM is 40.

Solution:

∵ LCM × GCF = 20 × 40⇒ GCF(20, 40) = (20 × 40)/40 = 20Therefore, the greatest usual factor that 20 and 40 is 20.


Example 3: The product of two numbers is 800. If their GCF is 20, what is their LCM?

Solution:

Given: GCF = 20 and product of number = 800∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 800/20Therefore, the LCM is 40.


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FAQs ~ above GCF the 20 and 40

What is the GCF the 20 and 40?

The GCF that 20 and 40 is 20. To calculate the greatest typical factor that 20 and also 40, we require to element each number (factors that 20 = 1, 2, 4, 5, 10, 20; components of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the greatest element that exactly divides both 20 and also 40, i.e., 20.

How to uncover the GCF the 20 and 40 by prime Factorization?

To find the GCF of 20 and 40, we will uncover the prime factorization that the given numbers, i.e. 20 = 2 × 2 × 5; 40 = 2 × 2 × 2 × 5.⇒ since 2, 2, 5 are common terms in the element factorization the 20 and 40. Hence, GCF(20, 40) = 2 × 2 × 5 = 20☛ What is a prime Number?

What space the approaches to discover GCF of 20 and also 40?

There are three frequently used methods to find the GCF the 20 and also 40.

By prime FactorizationBy Euclidean AlgorithmBy long Division

How to find the GCF of 20 and 40 through Long division Method?

To find the GCF that 20, 40 making use of long department method, 40 is divided by 20. The matching divisor (20) as soon as remainder equates to 0 is taken as GCF.

What is the Relation in between LCM and GCF the 20, 40?

The following equation have the right to be provided to refer the relation between Least usual Multiple and also GCF of 20 and also 40, i.e. GCF × LCM = 20 × 40.

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If the GCF of 40 and 20 is 20, discover its LCM.

GCF(40, 20) × LCM(40, 20) = 40 × 20Since the GCF of 40 and also 20 = 20⇒ 20 × LCM(40, 20) = 800Therefore, LCM = 40☛ GCF Calculator