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GCF of 36 and 45

GCF of 36 and 45 is the largest possible number that divides 36 and 45 exactly without any 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 methods to find the GCF of 36 and 45 - prime factorization, Euclidean algorithm, and long division.

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

What is GCF of 36 and 45?

Answer: GCF of 36 and 45 is 9.

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 remainder.

Methods to Find GCF of 36 and 45

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

Using Euclid's Algorithm
Prime Factorization Method
Listing Common Factors

GCF of 36 and 45 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and 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)

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

GCF of 36 and 45 by Prime Factorization

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

GCF of 36 and 45 by Listing Common Factors

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

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

☛ Also Check:

GCF of 36 and 45 Examples

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

Solution:

∵ LCM × GCF = 36 × 45
⇒ GCF(36, 45) = (36 × 45)/180 = 9
Therefore, the greatest common factor of 36 and 45 is 9.
Example 2: For two numbers, GCF = 9 and LCM = 180. If one number is 45, find 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 = 36
Therefore, the other number is 36.
Example 3: The product of two 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 = 1620/9
Therefore, 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 45 is 9. To calculate the greatest common factor (GCF) of 36 and 45, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 45 = 1, 3, 5, 9, 15, 45) and choose the greatest factor that exactly divides both 36 and 45, i.e., 9.

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

To find the GCF of 36, 45 using long division method, 45 is divided by 36. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

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

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

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

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

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

The following equation can be used to express the relation between LCM and GCF of 36 and 45, i.e. GCF × LCM = 36 × 45.

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

There are three commonly used methods to find the GCF of 36 and 45.

By Long Division
By Prime Factorization
By Euclidean Algorithm

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