GCF that 15 and 60 is the largest feasible number the divides 15 and also 60 exactly without any kind of remainder. The components of 15 and also 60 are 1, 3, 5, 15 and also 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 respectively. There room 3 frequently used techniques to uncover the GCF that 15 and also 60 - Euclidean algorithm, long division, and prime factorization.

You are watching: Greatest common factor of 15 and 60

1.GCF of 15 and 60
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF that 15 and 60 is 15.

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Explanation:

The GCF of two non-zero integers, x(15) and y(60), is the best positive integer m(15) the divides both x(15) and also y(60) without any type of remainder.


The approaches to discover the GCF of 15 and 60 are explained below.

Prime administrate MethodListing common FactorsLong division Method

GCF of 15 and also 60 by prime Factorization

Prime administer of 15 and also 60 is (3 × 5) and (2 × 2 × 3 × 5) respectively. Together visible, 15 and also 60 have common prime factors. Hence, the GCF that 15 and 60 is 3 × 5 = 15.

GCF that 15 and also 60 by Listing typical Factors

Factors the 15: 1, 3, 5, 15Factors the 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

There space 4 common factors of 15 and 60, that room 1, 3, 5, and also 15. Therefore, the greatest common factor the 15 and 60 is 15.

GCF of 15 and also 60 by lengthy Division

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GCF of 15 and also 60 is the divisor the we acquire when the remainder becomes 0 after doing long division repeatedly.

Step 2: due to the fact that the remainder = 0, the divisor (15) is the GCF the 15 and 60.

The corresponding divisor (15) is the GCF of 15 and also 60.

☛ likewise Check:


GCF the 15 and 60 Examples


Example 1: discover the greatest number the divides 15 and also 60 exactly.

Solution:

The biggest number the divides 15 and 60 exactly is their greatest usual factor, i.e. GCF that 15 and also 60.⇒ components of 15 and also 60:

Factors the 15 = 1, 3, 5, 15Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Therefore, the GCF of 15 and also 60 is 15.


Example 2: discover the GCF the 15 and also 60, if your LCM is 60.

Solution:

∵ LCM × GCF = 15 × 60⇒ GCF(15, 60) = (15 × 60)/60 = 15Therefore, the greatest usual factor the 15 and also 60 is 15.


Example 3: For 2 numbers, GCF = 15 and LCM = 60. If one number is 15, uncover the other number.

Solution:

Given: GCF (y, 15) = 15 and LCM (y, 15) = 60∵ GCF × LCM = 15 × (y)⇒ y = (GCF × LCM)/15⇒ y = (15 × 60)/15⇒ y = 60Therefore, the other number is 60.


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FAQs on GCF that 15 and also 60

What is the GCF that 15 and also 60?

The GCF of 15 and 60 is 15. To calculation the greatest usual factor of 15 and also 60, we need to element each number (factors that 15 = 1, 3, 5, 15; components of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) and also choose the greatest aspect that precisely divides both 15 and 60, i.e., 15.

What is the Relation between LCM and also GCF the 15, 60?

The adhering to equation can be offered to refer the relation in between LCM and GCF of 15 and also 60, i.e. GCF × LCM = 15 × 60.

How to uncover the GCF that 15 and also 60 by prime Factorization?

To uncover the GCF of 15 and also 60, we will discover the element factorization that the given numbers, i.e. 15 = 3 × 5; 60 = 2 × 2 × 3 × 5.⇒ since 3, 5 are typical terms in the prime factorization the 15 and 60. Hence, GCF(15, 60) = 3 × 5 = 15☛ prime Numbers

How to discover the GCF the 15 and 60 through Long department Method?

To discover the GCF of 15, 60 using long division method, 60 is separated by 15. The corresponding divisor (15) once remainder amounts to 0 is taken as GCF.

If the GCF the 60 and 15 is 15, uncover its LCM.

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GCF(60, 15) × LCM(60, 15) = 60 × 15Since the GCF of 60 and 15 = 15⇒ 15 × LCM(60, 15) = 900Therefore, LCM = 60☛ GCF Calculator

What are the methods to discover GCF of 15 and also 60?

There room three commonly used approaches to uncover the GCF that 15 and also 60.