GCF of 32 and 45 is the largest possible number that divides 32 and also 45 exactly without any kind of remainder. The factors of 32 and also 45 space 1, 2, 4, 8, 16, 32 and 1, 3, 5, 9, 15, 45 respectively. There room 3 commonly used methods to uncover the GCF that 32 and also 45 - prime factorization, Euclidean algorithm, and also long division.

You are watching: What is the greatest common factor of 32 and 45

1.GCF the 32 and also 45
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF that 32 and 45 is 1.

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Explanation:

The GCF of two non-zero integers, x(32) and also y(45), is the best positive essence m(1) that divides both x(32) and y(45) without any type of remainder.


The techniques to find the GCF the 32 and also 45 are explained below.

Prime factorization MethodListing common FactorsLong division Method

GCF that 32 and also 45 by prime Factorization

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Prime administrate of 32 and 45 is (2 × 2 × 2 × 2 × 2) and (3 × 3 × 5) respectively. Together visible, there space no common prime factors between 32 and 45, i.e. They room coprime. Hence, the GCF of 32 and 45 will be 1.

GCF that 32 and also 45 through Listing common Factors

Factors that 32: 1, 2, 4, 8, 16, 32Factors of 45: 1, 3, 5, 9, 15, 45

Since, 1 is the only common factor between 32 and also 45. The Greatest typical Factor of 32 and 45 is 1.

GCF the 32 and also 45 by lengthy Division

GCF the 32 and 45 is the divisor the we obtain when the remainder becomes 0 after doing long department repeatedly.

Step 2: because the remainder ≠ 0, we will certainly divide the divisor of step 1 (32) by the remainder (13).Step 3: Repeat this process until the remainder = 0.

The equivalent divisor (1) is the GCF that 32 and 45.

☛ likewise Check:


GCF the 32 and also 45 Examples


Example 1: discover the GCF of 32 and also 45, if their LCM is 1440.

Solution:

∵ LCM × GCF = 32 × 45⇒ GCF(32, 45) = (32 × 45)/1440 = 1Therefore, the greatest usual factor of 32 and also 45 is 1.


Example 2: The product of 2 numbers is 1440. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 1440∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 1440/1Therefore, the LCM is 1440.


Example 3: For two numbers, GCF = 1 and also LCM = 1440. If one number is 45, find the other number.

Solution:

Given: GCF (y, 45) = 1 and also LCM (y, 45) = 1440∵ GCF × LCM = 45 × (y)⇒ y = (GCF × LCM)/45⇒ y = (1 × 1440)/45⇒ y = 32Therefore, the various other number is 32.


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FAQs ~ above GCF that 32 and also 45

What is the GCF that 32 and also 45?

The GCF the 32 and also 45 is 1. To calculation the greatest usual factor (GCF) the 32 and also 45, we require to aspect each number (factors the 32 = 1, 2, 4, 8, 16, 32; determinants of 45 = 1, 3, 5, 9, 15, 45) and also choose the greatest factor that specifically divides both 32 and also 45, i.e., 1.

How to discover the GCF that 32 and 45 by Long department Method?

To discover the GCF the 32, 45 making use of long division method, 45 is divided by 32. The matching divisor (1) when remainder equals 0 is taken together GCF.

What is the Relation in between LCM and also GCF that 32, 45?

The adhering to equation have the right to be used to refer the relation in between Least typical Multiple (LCM) and also GCF of 32 and also 45, i.e. GCF × LCM = 32 × 45.

What space the techniques to find GCF of 32 and 45?

There are three frequently used approaches to uncover the GCF of 32 and 45.

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By long DivisionBy element FactorizationBy Listing typical Factors

How to discover the GCF the 32 and 45 by element Factorization?

To find the GCF that 32 and 45, we will find the element factorization the the provided numbers, i.e. 32 = 2 × 2 × 2 × 2 × 2; 45 = 3 × 3 × 5.⇒ there is no usual prime variable for 32 and 45. Hence, GCF (32, 45) = 1.☛ What space Prime Numbers?

If the GCF the 45 and also 32 is 1, discover its LCM.

GCF(45, 32) × LCM(45, 32) = 45 × 32Since the GCF of 45 and 32 = 1⇒ 1 × LCM(45, 32) = 1440Therefore, LCM = 1440☛ GCF Calculator