GCF that 10 and 15 is the largest feasible number the divides 10 and 15 precisely without any type of remainder. The determinants of 10 and also 15 are 1, 2, 5, 10 and also 1, 3, 5, 15 respectively. There room 3 generally used approaches to discover the GCF the 10 and 15 - Euclidean algorithm, prime factorization, and also long division.

You are watching: Greatest common factor of 10 and 15

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

Answer: GCF the 10 and 15 is 5.

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Explanation:

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


The approaches to find the GCF of 10 and 15 are defined below.

Listing typical FactorsLong department MethodPrime factorization Method

GCF that 10 and 15 through Listing typical Factors

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

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

GCF the 10 and 15 by lengthy Division

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GCF that 10 and also 15 is the divisor the we get when the remainder becomes 0 ~ doing long division repeatedly.

Step 2: since the remainder ≠ 0, we will certainly divide the divisor of step 1 (10) through the remainder (5).Step 3: Repeat this procedure until the remainder = 0.

The corresponding divisor (5) is the GCF that 10 and 15.

GCF the 10 and also 15 by prime Factorization

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Prime administer of 10 and 15 is (2 × 5) and (3 × 5) respectively. Together visible, 10 and also 15 have actually only one usual prime aspect i.e. 5. Hence, the GCF the 10 and 15 is 5.

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GCF the 10 and also 15 Examples


Example 1: uncover the best number that divides 10 and 15 exactly.

Solution:

The best number that divides 10 and also 15 specifically is their greatest typical factor, i.e. GCF of 10 and also 15.⇒ factors of 10 and also 15:

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

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


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

Solution:

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


Example 3: For 2 numbers, GCF = 5 and also LCM = 30. If one number is 15, uncover the various other number.

Solution:

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


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FAQs ~ above GCF of 10 and also 15

What is the GCF of 10 and 15?

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

How to find the GCF of 10 and also 15 through Long department Method?

To uncover the GCF that 10, 15 using long department method, 15 is split by 10. The matching divisor (5) once remainder amounts to 0 is taken together GCF.

What space the methods to find GCF that 10 and 15?

There space three frequently used techniques to uncover the GCF that 10 and 15.

By long DivisionBy Listing common FactorsBy prime Factorization

How to discover the GCF the 10 and also 15 by element Factorization?

To uncover the GCF of 10 and 15, we will discover the prime factorization of the given numbers, i.e. 10 = 2 × 5; 15 = 3 × 5.⇒ due to the fact that 5 is the only typical prime factor of 10 and also 15. Hence, GCF (10, 15) = 5.☛ prime Number

What is the Relation in between LCM and also GCF that 10, 15?

The following equation deserve to be provided to to express the relation in between LCM (Least usual Multiple) and GCF the 10 and 15, i.e. GCF × LCM = 10 × 15.

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If the GCF that 15 and also 10 is 5, find its LCM.

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