GCF the 10 and also 15 is the largest feasible number that divides 10 and 15 specifically without any kind of remainder. The factors of 10 and 15 room 1, 2, 5, 10 and also 1, 3, 5, 15 respectively. There space 3 commonly used methods to uncover the GCF of 10 and also 15 - Euclidean algorithm, element factorization, and also long division.

You are watching: What is the greatest common factor of 10 and 15

1.GCF the 10 and also 15
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF of 10 and 15 is 5.

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Explanation:

The GCF of two non-zero integers, x(10) and y(15), is the biggest positive essence m(5) that divides both x(10) and also y(15) without any type of remainder.


The techniques to uncover the GCF of 10 and 15 are described below.

Listing common FactorsLong division MethodPrime factorization Method

GCF of 10 and 15 by Listing typical Factors

Factors that 10: 1, 2, 5, 10Factors of 15: 1, 3, 5, 15

There space 2 usual factors of 10 and 15, that room 1 and also 5. Therefore, the greatest usual factor the 10 and also 15 is 5.

GCF of 10 and also 15 by lengthy Division

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GCF the 10 and 15 is the divisor that we acquire when the remainder becomes 0 after ~ doing long department repeatedly.

Step 2: due to the fact that the remainder ≠ 0, we will divide the divisor of action 1 (10) by the remainder (5).Step 3: Repeat this procedure until the remainder = 0.

The equivalent divisor (5) is the GCF of 10 and also 15.

GCF the 10 and also 15 by element Factorization

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Prime factorization of 10 and also 15 is (2 × 5) and also (3 × 5) respectively. Together visible, 10 and 15 have only one common prime variable i.e. 5. Hence, the GCF that 10 and 15 is 5.

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GCF the 10 and also 15 Examples


Example 1: uncover the biggest number the divides 10 and also 15 exactly.

Solution:

The greatest number the divides 10 and 15 specifically is your greatest typical factor, i.e. GCF of 10 and also 15.⇒ determinants of 10 and 15:

Factors the 10 = 1, 2, 5, 10Factors the 15 = 1, 3, 5, 15

Therefore, the GCF of 10 and also 15 is 5.


Example 2: discover the GCF of 10 and also 15, if their LCM is 30.

Solution:

∵ LCM × GCF = 10 × 15⇒ GCF(10, 15) = (10 × 15)/30 = 5Therefore, the greatest usual factor of 10 and also 15 is 5.


Example 3: For two numbers, GCF = 5 and also LCM = 30. If one number is 15, uncover the various other number.

Solution:

Given: GCF (z, 15) = 5 and LCM (z, 15) = 30∵ GCF × LCM = 15 × (z)⇒ z = (GCF × LCM)/15⇒ z = (5 × 30)/15⇒ z = 10Therefore, the other number is 10.


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FAQs ~ above GCF that 10 and 15

What is the GCF of 10 and also 15?

The GCF the 10 and 15 is 5. To calculate the greatest common factor (GCF) of 10 and 15, we require to element each number (factors of 10 = 1, 2, 5, 10; determinants of 15 = 1, 3, 5, 15) and choose the greatest element that specifically divides both 10 and 15, i.e., 5.

How to discover the GCF that 10 and 15 through Long division Method?

To find the GCF of 10, 15 using long department method, 15 is divided by 10. The equivalent divisor (5) once remainder amounts to 0 is taken as GCF.

What space the approaches to uncover GCF of 10 and also 15?

There are three typically used methods to find the GCF the 10 and also 15.

By long DivisionBy Listing usual FactorsBy element Factorization

How to uncover the GCF that 10 and 15 by element Factorization?

To uncover the GCF that 10 and also 15, we will uncover the prime factorization that the provided numbers, i.e. 10 = 2 × 5; 15 = 3 × 5.⇒ because 5 is the only usual prime variable of 10 and also 15. Hence, GCF (10, 15) = 5.☛ prime Number

What is the Relation between LCM and GCF of 10, 15?

The adhering to equation have the right to be used to express the relation in between LCM (Least typical Multiple) and also GCF of 10 and also 15, i.e. GCF × LCM = 10 × 15.

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If the GCF the 15 and 10 is 5, uncover its LCM.

GCF(15, 10) × LCM(15, 10) = 15 × 10Since the GCF of 15 and 10 = 5⇒ 5 × LCM(15, 10) = 150Therefore, LCM = 30☛ Greatest common Factor Calculator