GCF that 15 and also 35 is the largest feasible number the divides 15 and 35 precisely without any remainder. The factors of 15 and also 35 are 1, 3, 5, 15 and also 1, 5, 7, 35 respectively. There space 3 typically used approaches to uncover the GCF that 15 and also 35 - Euclidean algorithm, prime factorization, and long division.

You are watching: What is the 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 of 15 and 35 is 5.

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Explanation:

The GCF of two non-zero integers, x(15) and y(35), is the biggest positive integer m(5) that divides both x(15) and also y(35) without any remainder.


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

Listing common FactorsUsing Euclid's AlgorithmPrime administrate Method

GCF that 15 and 35 through Listing usual Factors

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

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

GCF the 15 and 35 through Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mode Y)where X > Y and mod is the modulo operator.

Here X = 35 and 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|, whereby X ≠ 0)

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

GCF that 15 and 35 by element Factorization

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

☛ additionally Check:


GCF the 15 and 35 Examples


Example 1: For 2 numbers, GCF = 5 and LCM = 105. If one number is 35, uncover the various 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 other number is 15.


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

Solution:

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


Example 3: uncover 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 35 is 5.


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FAQs on GCF that 15 and 35

What is the GCF that 15 and also 35?

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

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

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

What are the approaches to discover GCF the 15 and also 35?

There are three frequently used approaches to find the GCF the 15 and 35.

By prime FactorizationBy long DivisionBy Euclidean Algorithm

If the GCF of 35 and 15 is 5, find its LCM.

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

How to find the GCF that 15 and also 35 by Long division Method?

To discover the GCF of 15, 35 making use of long division method, 35 is split by 15. The corresponding divisor (5) as soon as remainder equates to 0 is taken as GCF.

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What is the Relation in between LCM and GCF of 15, 35?

The adhering to equation deserve to be supplied to refer the relation between Least common Multiple (LCM) and GCF the 15 and also 35, i.e. GCF × LCM = 15 × 35.