GCF that 32 and also 45 is the largest possible number the divides 32 and 45 precisely without any type of remainder. The factors of 32 and also 45 are 1, 2, 4, 8, 16, 32 and 1, 3, 5, 9, 15, 45 respectively. There are 3 frequently used techniques to discover the GCF that 32 and also 45 - prime factorization, Euclidean algorithm, and also long division.

You are watching: What is the gcf of 32 and 45

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

Answer: GCF of 32 and also 45 is 1.

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Explanation:

The GCF of 2 non-zero integers, x(32) and y(45), is the biggest positive essence m(1) the divides both x(32) and y(45) without any kind of remainder.


The techniques to discover the GCF of 32 and 45 are described below.

Prime administer MethodListing usual FactorsLong department Method

GCF that 32 and 45 by element Factorization

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

GCF the 32 and 45 through Listing typical Factors

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

Since, 1 is the only usual factor in between 32 and also 45. The Greatest usual Factor the 32 and also 45 is 1.

GCF the 32 and also 45 by lengthy Division

GCF of 32 and 45 is the divisor that we acquire when the remainder i do not care 0 after doing long division repeatedly.

Step 2: due to the fact that the remainder ≠ 0, we will certainly divide the divisor of step 1 (32) by the remainder (13).Step 3: Repeat this procedure until the remainder = 0.

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

☛ additionally Check:


GCF of 32 and also 45 Examples


Example 1: find the GCF the 32 and also 45, if your LCM is 1440.

Solution:

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


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

Solution:

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


Example 3: For 2 numbers, GCF = 1 and LCM = 1440. If one number is 45, uncover the various 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 top top GCF that 32 and 45

What is the GCF of 32 and 45?

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

How to find the GCF that 32 and also 45 through Long division Method?

To uncover the GCF the 32, 45 utilizing long department method, 45 is divided by 32. The equivalent divisor (1) when remainder amounts to 0 is taken together GCF.

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

The complying with equation can be used to express the relation between Least common Multiple (LCM) and also GCF the 32 and also 45, i.e. GCF × LCM = 32 × 45.

What space the approaches to find GCF that 32 and also 45?

There space three commonly used methods to find the GCF that 32 and 45.

See more: How Many Valence Electron Does Oxygen Have, How Many Valence Electrons Does Oxygen Atom Has

By long DivisionBy prime FactorizationBy Listing usual Factors

How to discover the GCF the 32 and also 45 by prime Factorization?

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

If the GCF of 45 and 32 is 1, find its LCM.

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