GCF of 36 and also 45 is the largest possible number that divides 36 and 45 precisely without any remainder. The determinants of 36 and also 45 room 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 3, 5, 9, 15, 45 respectively. There room 3 frequently used techniques to find the GCF the 36 and also 45 - element factorization, Euclidean algorithm, and long division.

You are watching: What is the gcf of 36 and 45

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

Answer: GCF the 36 and 45 is 9.

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Explanation:

The GCF of 2 non-zero integers, x(36) and also y(45), is the greatest positive creature m(9) the divides both x(36) and also y(45) without any kind of remainder.


Let's look in ~ the various methods for finding the GCF of 36 and 45.

Using Euclid's AlgorithmPrime administrate MethodListing common Factors

GCF that 36 and 45 through Euclidean Algorithm

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

Here X = 45 and also Y = 36

GCF(45, 36) = GCF(36, 45 mode 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)

Therefore, the value of GCF of 36 and also 45 is 9.

GCF that 36 and 45 by element Factorization

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

GCF that 36 and 45 through Listing usual Factors

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

There are 3 typical factors of 36 and 45, that are 1, 3, and also 9. Therefore, the greatest usual factor that 36 and 45 is 9.

☛ also Check:


GCF the 36 and also 45 Examples


Example 1: uncover the GCF the 36 and 45, if their LCM is 180.

Solution:

∵ LCM × GCF = 36 × 45⇒ GCF(36, 45) = (36 × 45)/180 = 9Therefore, the greatest typical factor that 36 and 45 is 9.


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

Solution:

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


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

Solution:

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


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FAQs top top GCF that 36 and also 45

What is the GCF that 36 and also 45?

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

How to uncover the GCF that 36 and also 45 through Long department Method?

To discover the GCF of 36, 45 utilizing long division method, 45 is separated by 36. The equivalent divisor (9) as soon as remainder amounts to 0 is taken as GCF.

If the GCF that 45 and also 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) = 1620Therefore, LCM = 180☛ Greatest common Factor Calculator

How to discover the GCF of 36 and 45 by element Factorization?

To discover the GCF the 36 and also 45, we will uncover the element factorization of the offered numbers, i.e. 36 = 2 × 2 × 3 × 3; 45 = 3 × 3 × 5.⇒ due to the fact that 3, 3 are common terms in the prime factorization the 36 and also 45. Hence, GCF(36, 45) = 3 × 3 = 9☛ element Number

What is the Relation in between LCM and GCF that 36, 45?

The complying with equation deserve to be supplied to express the relation between LCM and also GCF of 36 and also 45, i.e. GCF × LCM = 36 × 45.

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What room the methods to uncover GCF of 36 and 45?

There are three frequently used methods to uncover the GCF the 36 and also 45.