GCF the 15 and also 35 is the largest feasible number the divides 15 and 35 precisely without any kind of remainder. The components of 15 and also 35 room 1, 3, 5, 15 and also 1, 5, 7, 35 respectively. There room 3 frequently used methods to uncover the GCF of 15 and 35 - Euclidean algorithm, prime factorization, and also long division.

You are watching: Greatest common factor of 15 and 35

1.GCF of 15 and also 35
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF the 15 and 35 is 5.

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Explanation:

The GCF of 2 non-zero integers, x(15) and y(35), is the biggest positive essence m(5) the divides both x(15) and y(35) without any type of remainder.


The approaches to uncover the GCF of 15 and 35 are explained below.

Listing typical FactorsUsing Euclid's AlgorithmPrime administrate Method

GCF the 15 and also 35 through Listing usual Factors

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Factors of 15: 1, 3, 5, 15Factors of 35: 1, 5, 7, 35

There room 2 typical factors of 15 and 35, that room 1 and also 5. Therefore, the greatest common factor that 15 and also 35 is 5.

GCF of 15 and also 35 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 = 35 and also Y = 15

GCF(35, 15) = GCF(15, 35 mode 15) = GCF(15, 5)GCF(15, 5) = GCF(5, 15 mod 5) = GCF(5, 0)GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the worth of GCF of 15 and also 35 is 5.

GCF of 15 and 35 by prime Factorization

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Prime administer of 15 and 35 is (3 × 5) and also (5 × 7) respectively. Together visible, 15 and also 35 have only one usual prime variable i.e. 5. Hence, the GCF that 15 and 35 is 5.

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GCF of 15 and also 35 Examples


Example 1: For 2 numbers, GCF = 5 and LCM = 105. If one number is 35, uncover the other number.

Solution:

Given: GCF (y, 35) = 5 and also LCM (y, 35) = 105∵ GCF × LCM = 35 × (y)⇒ y = (GCF × LCM)/35⇒ y = (5 × 105)/35⇒ y = 15Therefore, the various other number is 15.


Example 2: The product of 2 numbers is 525. If your GCF is 5, what is your LCM?

Solution:

Given: GCF = 5 and also product of number = 525∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 525/5Therefore, the LCM is 105.


Example 3: discover the GCF the 15 and also 35, if your LCM is 105.

Solution:

∵ LCM × GCF = 15 × 35⇒ GCF(15, 35) = (15 × 35)/105 = 5Therefore, the greatest common factor that 15 and also 35 is 5.


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FAQs on GCF of 15 and also 35

What is the GCF of 15 and 35?

The GCF the 15 and also 35 is 5. To calculate the GCF of 15 and 35, we require to element each number (factors of 15 = 1, 3, 5, 15; determinants of 35 = 1, 5, 7, 35) and choose the greatest element that exactly divides both 15 and also 35, i.e., 5.

How to uncover the GCF the 15 and also 35 by prime Factorization?

To discover the GCF the 15 and 35, us will find the prime factorization the the offered numbers, i.e. 15 = 3 × 5; 35 = 5 × 7.⇒ due to the fact that 5 is the only usual prime variable of 15 and 35. Hence, GCF (15, 35) = 5.☛ What is a element Number?

What space the methods to discover GCF the 15 and also 35?

There space three commonly used techniques to discover the GCF that 15 and also 35.

By element FactorizationBy long DivisionBy Euclidean Algorithm

If the GCF the 35 and also 15 is 5, discover its LCM.

GCF(35, 15) × LCM(35, 15) = 35 × 15Since the GCF that 35 and also 15 = 5⇒ 5 × LCM(35, 15) = 525Therefore, LCM = 105☛ Greatest common Factor Calculator

How to discover the GCF the 15 and 35 through Long division Method?

To uncover the GCF the 15, 35 using long division method, 35 is separated by 15. The equivalent divisor (5) when remainder equals 0 is taken together GCF.

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What is the Relation between LCM and also GCF that 15, 35?

The following equation can be used to refer the relation in between Least usual Multiple (LCM) and GCF that 15 and 35, i.e. GCF × LCM = 15 × 35.