GCF of 45 and also 60 is the largest possible number the divides 45 and also 60 precisely without any type of remainder. The factors of 45 and 60 room 1, 3, 5, 9, 15, 45 and 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 respectively. There room 3 typically used methods to find the GCF of 45 and 60 - Euclidean algorithm, long division, and prime factorization.

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1.GCF of 45 and also 60
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF that 45 and 60 is 15.

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Explanation:

The GCF of 2 non-zero integers, x(45) and y(60), is the greatest positive creature m(15) that divides both x(45) and also y(60) without any kind of remainder.


The approaches to uncover the GCF of 45 and 60 are explained below.

Long division MethodPrime administer MethodListing typical Factors

GCF that 45 and 60 by lengthy Division

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GCF of 45 and also 60 is the divisor the we gain when the remainder becomes 0 after doing long division repeatedly.

Step 2: because the remainder ≠ 0, we will divide the divisor of step 1 (45) by the remainder (15).Step 3: Repeat this process until the remainder = 0.

The matching divisor (15) is the GCF of 45 and also 60.

GCF of 45 and 60 by element Factorization

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Prime factorization of 45 and 60 is (3 × 3 × 5) and (2 × 2 × 3 × 5) respectively. Together visible, 45 and also 60 have usual prime factors. Hence, the GCF that 45 and also 60 is 3 × 5 = 15.

GCF that 45 and 60 through Listing usual Factors

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Factors that 45: 1, 3, 5, 9, 15, 45Factors that 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

There are 4 typical factors the 45 and also 60, that room 1, 3, 5, and 15. Therefore, the greatest usual factor the 45 and 60 is 15.

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GCF that 45 and 60 Examples


Example 1: The product of 2 numbers is 2700. If your GCF is 15, what is their LCM?

Solution:

Given: GCF = 15 and product of numbers = 2700∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 2700/15Therefore, the LCM is 180.


Example 2: For two numbers, GCF = 15 and also LCM = 180. If one number is 45, find the other number.

Solution:

Given: GCF (x, 45) = 15 and also LCM (x, 45) = 180∵ GCF × LCM = 45 × (x)⇒ x = (GCF × LCM)/45⇒ x = (15 × 180)/45⇒ x = 60Therefore, the other number is 60.


Example 3: uncover the greatest number that divides 45 and also 60 exactly.

Solution:

The greatest number that divides 45 and 60 specifically is your greatest common factor, i.e. GCF of 45 and also 60.⇒ factors of 45 and 60:

Factors that 45 = 1, 3, 5, 9, 15, 45Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Therefore, the GCF that 45 and also 60 is 15.


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FAQs top top GCF that 45 and also 60

What is the GCF the 45 and also 60?

The GCF of 45 and also 60 is 15. To calculate the GCF (Greatest usual Factor) of 45 and 60, we need to element each number (factors the 45 = 1, 3, 5, 9, 15, 45; components of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) and choose the greatest variable that precisely divides both 45 and also 60, i.e., 15.

How to uncover the GCF the 45 and also 60 by prime Factorization?

To discover the GCF of 45 and also 60, us will discover the prime factorization of the provided numbers, i.e. 45 = 3 × 3 × 5; 60 = 2 × 2 × 3 × 5.⇒ due to the fact that 3, 5 are common terms in the prime factorization the 45 and also 60. Hence, GCF(45, 60) = 3 × 5 = 15☛ prime Number

What is the Relation in between LCM and GCF of 45, 60?

The adhering to equation deserve to be used to refer the relation in between Least typical Multiple and GCF the 45 and also 60, i.e. GCF × LCM = 45 × 60.

If the GCF of 60 and also 45 is 15, find its LCM.

GCF(60, 45) × LCM(60, 45) = 60 × 45Since the GCF that 60 and 45 = 15⇒ 15 × LCM(60, 45) = 2700Therefore, LCM = 180☛ Greatest common Factor Calculator

How to find the GCF of 45 and 60 by Long division Method?

To find the GCF of 45, 60 making use of long division method, 60 is split by 45. The equivalent divisor (15) as soon as remainder equals 0 is taken together GCF.

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What space the techniques to discover GCF that 45 and 60?

There are three commonly used approaches to find the GCF the 45 and 60.