GCF that 15 and 25 is the largest feasible number the divides 15 and also 25 exactly without any type of remainder. The determinants of 15 and 25 room 1, 3, 5, 15 and also 1, 5, 25 respectively. There room 3 typically used methods to discover the GCF of 15 and also 25 - prime factorization, long division, and also Euclidean algorithm.

You are watching: Greatest common factor of 15 and 25

1.GCF that 15 and 25
2.List the 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 best positive creature m(5) that divides both x(15) and also y(25) without any type of remainder.


The methods to find the GCF that 15 and also 25 are explained below.

Using Euclid's AlgorithmListing typical FactorsPrime factorization Method

GCF of 15 and also 25 by Euclidean Algorithm

As every the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod 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 mode 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 the 15 and 25 is 5.

GCF of 15 and also 25 through Listing typical Factors

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

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

GCF the 15 and 25 by element Factorization

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

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GCF of 15 and also 25 Examples


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

Solution:

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


Example 2: For 2 numbers, GCF = 5 and also LCM = 75. If one number is 15, uncover 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: discover the GCF that 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 that 15 and 25 is 5.


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FAQs top top GCF that 15 and 25

What is the GCF of 15 and 25?

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

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

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

What room the approaches to discover GCF the 15 and also 25?

There are three commonly used methods to find the GCF of 15 and 25.

By Euclidean AlgorithmBy prime FactorizationBy long Division

How to find the GCF that 15 and 25 through Long division Method?

To find the GCF of 15, 25 making use of long division method, 25 is separated by 15. The matching divisor (5) as soon as remainder equates to 0 is taken as GCF.

See more: Which Of The Following Is A Seedless Vascular Plant S, Seedless Vascular Plants

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

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

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

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