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

You are watching: What is the gcf of 2 and 5

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

Answer: GCF of 2 and also 5 is 1.

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Explanation:

The GCF of two non-zero integers, x(2) and also y(5), is the greatest positive integer m(1) the divides both x(2) and also y(5) without any type of remainder.


Let's look at the various methods for finding the GCF the 2 and also 5.

Using Euclid's AlgorithmLong department MethodListing usual Factors

GCF the 2 and 5 by 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 = 5 and Y = 2

GCF(5, 2) = GCF(2, 5 mod 2) = GCF(2, 1)GCF(2, 1) = GCF(1, 2 mode 1) = GCF(1, 0)GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, whereby X ≠ 0)

Therefore, the worth of GCF of 2 and also 5 is 1.

GCF the 2 and 5 by lengthy Division

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GCF the 2 and 5 is the divisor the we get when the remainder becomes 0 after doing long division repeatedly.

Step 2: since the remainder ≠ 0, we will certainly divide the divisor of action 1 (2) by the remainder (1).Step 3: Repeat this procedure until the remainder = 0.

The equivalent divisor (1) is the GCF that 2 and 5.

GCF of 2 and also 5 by Listing usual Factors

Factors of 2: 1, 2Factors of 5: 1, 5

Since, 1 is the only common factor between 2 and 5. The Greatest common Factor that 2 and also 5 is 1.

☛ additionally Check:


GCF the 2 and also 5 Examples


Example 1: discover the GCF that 2 and also 5, if their LCM is 10.

Solution:

∵ LCM × GCF = 2 × 5⇒ GCF(2, 5) = (2 × 5)/10 = 1Therefore, the greatest common factor of 2 and 5 is 1.


Example 2: For two numbers, GCF = 1 and also LCM = 10. If one number is 2, find the various other number.

Solution:

Given: GCF (x, 2) = 1 and also LCM (x, 2) = 10∵ GCF × LCM = 2 × (x)⇒ x = (GCF × LCM)/2⇒ x = (1 × 10)/2⇒ x = 5Therefore, the various other number is 5.


Example 3: The product of two numbers is 10. If your GCF is 1, what is your LCM?

Solution:

Given: GCF = 1 and product of number = 10∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 10/1Therefore, the LCM is 10.


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FAQs ~ above GCF that 2 and also 5

What is the GCF the 2 and 5?

The GCF that 2 and 5 is 1. To calculation the GCF (Greatest common Factor) of 2 and also 5, we require to aspect each number (factors of 2 = 1, 2; determinants of 5 = 1, 5) and choose the greatest element that exactly divides both 2 and 5, i.e., 1.

If the GCF of 5 and also 2 is 1, uncover its LCM.

GCF(5, 2) × LCM(5, 2) = 5 × 2Since the GCF the 5 and 2 = 1⇒ 1 × LCM(5, 2) = 10Therefore, LCM = 10☛ GCF Calculator

How to find the GCF the 2 and 5 by prime Factorization?

To discover the GCF of 2 and 5, we will discover the prime factorization of the offered numbers, i.e. 2 = 2; 5 = 5.⇒ there is no typical prime element for 2 and 5. Hence, GCF (2, 5) = 1.☛ What space Prime Numbers?

What is the Relation between LCM and also GCF the 2, 5?

The complying with equation can be offered to refer the relation between LCM and also GCF of 2 and 5, i.e. GCF × LCM = 2 × 5.

How to discover the GCF the 2 and 5 through Long division Method?

To uncover the GCF the 2, 5 utilizing long department method, 5 is split by 2. The matching divisor (1) when remainder equals 0 is taken as GCF.

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What are the approaches to discover GCF of 2 and 5?

There room three typically used approaches to discover the GCF that 2 and 5.