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GCF of 18 and 45

GCF of 18 and 45 is the largest possible number that divides 18 and 45 exactly without any remainder. The factors of 18 and 45 are 1, 2, 3, 6, 9, 18 and 1, 3, 5, 9, 15, 45 respectively. There are 3 commonly used methods to find the GCF of 18 and 45 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 18 and 45
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 18 and 45?

Answer: GCF of 18 and 45 is 9.

Explanation:

The GCF of two non-zero integers, x(18) and y(45), is the greatest positive integer m(9) that divides both x(18) and y(45) without any remainder.

Methods to Find GCF of 18 and 45

The methods to find the GCF of 18 and 45 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 18 and 45 by Long Division

GCF of 18 and 45 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 45 (larger number) by 18 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (9).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (9) is the GCF of 18 and 45.

GCF of 18 and 45 by Listing Common Factors

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

There are 3 common factors of 18 and 45, that are 1, 3, and 9. Therefore, the greatest common factor of 18 and 45 is 9.

GCF of 18 and 45 by Prime Factorization

Prime factorization of 18 and 45 is (2 × 3 × 3) and (3 × 3 × 5) respectively. As visible, 18 and 45 have common prime factors. Hence, the GCF of 18 and 45 is 3 × 3 = 9.

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GCF of 18 and 45 Examples

Example 1: The product of two numbers is 810. If their GCF is 9, what is their LCM?

Solution:

Given: GCF = 9 and product of numbers = 810
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 810/9
Therefore, the LCM is 90.
Example 2: Find the GCF of 18 and 45, if their LCM is 90.

Solution:

∵ LCM × GCF = 18 × 45
⇒ GCF(18, 45) = (18 × 45)/90 = 9
Therefore, the greatest common factor of 18 and 45 is 9.
Example 3: For two numbers, GCF = 9 and LCM = 90. If one number is 18, find the other number.

Solution:

Given: GCF (z, 18) = 9 and LCM (z, 18) = 90
∵ GCF × LCM = 18 × (z)
⇒ z = (GCF × LCM)/18
⇒ z = (9 × 90)/18
⇒ z = 45
Therefore, the other number is 45.

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FAQs on GCF of 18 and 45

What is the GCF of 18 and 45?

The GCF of 18 and 45 is 9. To calculate the GCF of 18 and 45, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 45 = 1, 3, 5, 9, 15, 45) and choose the greatest factor that exactly divides both 18 and 45, i.e., 9.

If the GCF of 45 and 18 is 9, Find its LCM.

GCF(45, 18) × LCM(45, 18) = 45 × 18
Since the GCF of 45 and 18 = 9
⇒ 9 × LCM(45, 18) = 810
Therefore, LCM = 90
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What is the Relation Between LCM and GCF of 18, 45?

The following equation can be used to express the relation between LCM and GCF of 18 and 45, i.e. GCF × LCM = 18 × 45.

How to Find the GCF of 18 and 45 by Long Division Method?

To find the GCF of 18, 45 using long division method, 45 is divided by 18. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 18 and 45?

There are three commonly used methods to find the GCF of 18 and 45.

By Prime Factorization
By Listing Common Factors
By Long Division

How to Find the GCF of 18 and 45 by Prime Factorization?

To find the GCF of 18 and 45, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 45 = 3 × 3 × 5.
⇒ Since 3, 3 are common terms in the prime factorization of 18 and 45. Hence, GCF(18, 45) = 3 × 3 = 9
☛ What is a Prime Number?

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