GCF of 36 and 45 is the biggest possible number that divides 36 and 45 specifically without any kind of remainder. The factors of 36 and 45 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 3, 5, 9, 15, 45 respectively. There are 3 commonly used techniques to discover the GCF of 36 and also 45 - prime factorization, Euclidean algorithm, and lengthy department.

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1.GCF of 36 and also 45
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF of 36 and 45 is 9.

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Explanation:

The GCF of two non-zero integers, x(36) and y(45), is the greatest positive integer m(9) that divides both x(36) and y(45) without any kind of remainder.


Let's look at the different techniques for finding the GCF of 36 and 45.

Using Euclid's AlgorithmPrime Factorization MethodListing Usual Factors

GCF of 36 and also 45 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)where X > Y and also mod is the modulo operator.

Here X = 45 and Y = 36

GCF(45, 36) = GCF(36, 45 mod 36) = GCF(36, 9)GCF(36, 9) = GCF(9, 36 mod 9) = GCF(9, 0)GCF(9, 0) = 9 (∵ GCF(X, 0) = |X|, where X ≠ 0)

As such, the worth of GCF of 36 and 45 is 9.

GCF of 36 and 45 by Prime Factorization

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Prime factorization of 36 and 45 is (2 × 2 × 3 × 3) and also (3 × 3 × 5) respectively. As visible, 36 and 45 have actually common prime components. Hence, the GCF of 36 and also 45 is 3 × 3 = 9.

GCF of 36 and 45 by Listing Usual Factors

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Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36Factors of 45: 1, 3, 5, 9, 15, 45

Tright here are 3 widespread components of 36 and 45, that are 1, 3, and 9. Therefore, the biggest widespread factor of 36 and also 45 is 9.

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GCF of 36 and 45 Examples


Example 1: Find the GCF of 36 and also 45, if their LCM is 180.

Solution:

∵ LCM × GCF = 36 × 45⇒ GCF(36, 45) = (36 × 45)/180 = 9Therefore, the best widespread element of 36 and 45 is 9.


Example 2: For 2 numbers, GCF = 9 and LCM = 180. If one number is 45, uncover the other number.

Solution:

Given: GCF (z, 45) = 9 and also LCM (z, 45) = 180∵ GCF × LCM = 45 × (z)⇒ z = (GCF × LCM)/45⇒ z = (9 × 180)/45⇒ z = 36As such, the various other number is 36.


Example 3: The product of 2 numbers is 1620. If their GCF is 9, what is their LCM?

Solution:

Given: GCF = 9 and product of numbers = 1620∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 1620/9Thus, the LCM is 180.


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FAQs on GCF of 36 and 45

What is the GCF of 36 and 45?

The GCF of 36 and also 45 is 9. To calculate the best prevalent element (GCF) of 36 and also 45, we have to element each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 45 = 1, 3, 5, 9, 15, 45) and also choose the best factor that exactly divides both 36 and also 45, i.e., 9.

How to Find the GCF of 36 and 45 by Long Division Method?

To discover the GCF of 36, 45 using lengthy division method, 45 is split by 36. The equivalent divisor (9) when remainder amounts to 0 is taken as GCF.

If the GCF of 45 and 36 is 9, Find its LCM.

GCF(45, 36) × LCM(45, 36) = 45 × 36Since the GCF of 45 and also 36 = 9⇒ 9 × LCM(45, 36) = 1620Thus, LCM = 180☛ Greatest Common Factor Calculator

How to Find the GCF of 36 and also 45 by Prime Factorization?

To find the GCF of 36 and also 45, we will certainly find the prime factorization of the offered numbers, i.e. 36 = 2 × 2 × 3 × 3; 45 = 3 × 3 × 5.⇒ Because 3, 3 are common terms in the prime factorization of 36 and also 45. Hence, GCF(36, 45) = 3 × 3 = 9☛ Prime Number

What is the Relation Between LCM and also GCF of 36, 45?

The adhering to equation deserve to be supplied to expush the relation in between LCM and also GCF of 36 and 45, i.e. GCF × LCM = 36 × 45.

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What are the Methods to Find GCF of 36 and also 45?

Tbelow are three typically provided techniques to discover the GCF of 36 and also 45.