GCF the 15 and also 25 is the largest feasible number the divides 15 and 25 specifically without any remainder. The determinants of 15 and 25 are 1, 3, 5, 15 and also 1, 5, 25 respectively. There space 3 commonly used techniques to discover the GCF that 15 and 25 - prime factorization, long division, and also Euclidean algorithm.

You are watching: What is the gcf of 15 and 25

1.GCF of 15 and 25
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF the 15 and 25 is 5.

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Explanation:

The GCF of two non-zero integers, x(15) and y(25), is the biggest positive essence m(5) that divides both x(15) and also y(25) without any kind of remainder.


The techniques to discover the GCF the 15 and 25 are defined below.

Using Euclid's AlgorithmListing common FactorsPrime administrate Method

GCF the 15 and 25 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 = 25 and Y = 15

GCF(25, 15) = GCF(15, 25 mod 15) = GCF(15, 10)GCF(15, 10) = GCF(10, 15 mod 10) = GCF(10, 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 of 15 and also 25 is 5.

GCF the 15 and 25 by Listing typical Factors

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Factors the 15: 1, 3, 5, 15Factors of 25: 1, 5, 25

There space 2 common factors that 15 and also 25, that space 1 and 5. Therefore, the greatest typical factor that 15 and also 25 is 5.

GCF of 15 and also 25 by element Factorization

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Prime administer of 15 and 25 is (3 × 5) and (5 × 5) respectively. Together visible, 15 and also 25 have only one typical prime element i.e. 5. Hence, the GCF the 15 and 25 is 5.

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GCF of 15 and also 25 Examples


Example 1: The product of 2 numbers is 375. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and also product of number = 375∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 375/5Therefore, the LCM is 75.


Example 2: For 2 numbers, GCF = 5 and LCM = 75. If one number is 15, discover the various other number.

Solution:

Given: GCF (y, 15) = 5 and also LCM (y, 15) = 75∵ GCF × LCM = 15 × (y)⇒ y = (GCF × LCM)/15⇒ y = (5 × 75)/15⇒ y = 25Therefore, the various other number is 25.


Example 3: discover the GCF the 15 and also 25, if their LCM is 75.

Solution:

∵ LCM × GCF = 15 × 25⇒ GCF(15, 25) = (15 × 25)/75 = 5Therefore, the greatest usual factor the 15 and 25 is 5.


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FAQs top top GCF that 15 and 25

What is the GCF the 15 and 25?

The GCF the 15 and 25 is 5. To calculation the greatest typical factor that 15 and 25, we need to variable each number (factors the 15 = 1, 3, 5, 15; determinants of 25 = 1, 5, 25) and choose the greatest factor that exactly divides both 15 and also 25, i.e., 5.

What is the Relation in between LCM and also GCF that 15, 25?

The following equation deserve to be offered to express the relation between Least typical Multiple and also GCF the 15 and also 25, i.e. GCF × LCM = 15 × 25.

What are the methods to find GCF the 15 and also 25?

There are three commonly used techniques to uncover the GCF the 15 and also 25.

By Euclidean AlgorithmBy element FactorizationBy lengthy Division

How to discover the GCF of 15 and also 25 through Long division Method?

To discover the GCF that 15, 25 using long department method, 25 is split by 15. The equivalent divisor (5) once remainder equals 0 is taken together GCF.

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How to uncover the GCF of 15 and 25 by prime Factorization?

To find the GCF that 15 and 25, we will discover the prime factorization the the given numbers, i.e. 15 = 3 × 5; 25 = 5 × 5.⇒ because 5 is the only usual prime aspect of 15 and 25. Hence, GCF (15, 25) = 5.☛ prime Numbers

If the GCF of 25 and 15 is 5, discover its LCM.

GCF(25, 15) × LCM(25, 15) = 25 × 15Since the GCF of 25 and 15 = 5⇒ 5 × LCM(25, 15) = 375Therefore, LCM = 75☛ Greatest common Factor Calculator