GCF the 15 and 25 is the largest feasible number the divides 15 and also 25 exactly without any kind of remainder. The determinants of 15 and also 25 space 1, 3, 5, 15 and 1, 5, 25 respectively. There space 3 commonly used approaches to find the GCF the 15 and also 25 - element factorization, long division, and also Euclidean algorithm.

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

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

Answer: GCF the 15 and 25 is 5.

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Explanation:

The GCF of 2 non-zero integers, x(15) and also y(25), is the biggest positive integer m(5) the divides both x(15) and y(25) without any kind of remainder.


The methods to discover the GCF the 15 and also 25 are described below.

Using Euclid's AlgorithmListing common FactorsPrime administer Method

GCF the 15 and also 25 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 = 25 and also Y = 15

GCF(25, 15) = GCF(15, 25 mode 15) = GCF(15, 10)GCF(15, 10) = GCF(10, 15 mod 10) = GCF(10, 5)GCF(10, 5) = GCF(5, 10 mode 5) = GCF(5, 0)GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, whereby X ≠ 0)

Therefore, the worth of GCF the 15 and 25 is 5.

GCF of 15 and also 25 by Listing usual Factors

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

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

GCF that 15 and 25 by prime Factorization

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

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GCF the 15 and 25 Examples


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

Solution:

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


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

Solution:

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


Example 3: find the GCF the 15 and also 25, if your LCM is 75.

Solution:

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


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FAQs top top GCF that 15 and 25

What is the GCF that 15 and 25?

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

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

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

What room the techniques to discover GCF that 15 and 25?

There space three generally used methods to find the GCF of 15 and 25.

By Euclidean AlgorithmBy prime FactorizationBy lengthy Division

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

To find the GCF that 15, 25 utilizing long department method, 25 is separated by 15. The matching divisor (5) as soon as remainder equates to 0 is taken as GCF.

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

To uncover the GCF the 15 and 25, us will uncover the prime factorization the the provided numbers, i.e. 15 = 3 × 5; 25 = 5 × 5.⇒ because 5 is the only common prime factor of 15 and 25. Hence, GCF (15, 25) = 5.☛ element Numbers

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

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