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GCF of 18 and 90

GCF of 18 and 90 is the largest possible number that divides 18 and 90 exactly without any remainder. The factors of 18 and 90 are 1, 2, 3, 6, 9, 18 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 respectively. There are 3 commonly used methods to find the GCF of 18 and 90 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 18 and 90
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 18 and 90?

Answer: GCF of 18 and 90 is 18.

Explanation:

The GCF of two non-zero integers, x(18) and y(90), is the greatest positive integer m(18) that divides both x(18) and y(90) without any remainder.

Methods to Find GCF of 18 and 90

The methods to find the GCF of 18 and 90 are explained below.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 18 and 90 by Long Division

GCF of 18 and 90 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 90 (larger number) by 18 (smaller number).
Step 2: Since the remainder = 0, the divisor (18) is the GCF of 18 and 90.

The corresponding divisor (18) is the GCF of 18 and 90.

GCF of 18 and 90 by Listing Common Factors

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

There are 6 common factors of 18 and 90, that are 1, 2, 3, 6, 9, and 18. Therefore, the greatest common factor of 18 and 90 is 18.

GCF of 18 and 90 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 = 90 and Y = 18

GCF(90, 18) = GCF(18, 90 mod 18) = GCF(18, 0)
GCF(18, 0) = 18 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 18 and 90 is 18.

☛ Also Check:

GCF of 18 and 90 Examples

Example 1: Find the greatest number that divides 18 and 90 exactly.

Solution:

The greatest number that divides 18 and 90 exactly is their greatest common factor, i.e. GCF of 18 and 90.
⇒ Factors of 18 and 90:
- Factors of 18 = 1, 2, 3, 6, 9, 18
- Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Therefore, the GCF of 18 and 90 is 18.
Example 2: The product of two numbers is 1620. If their GCF is 18, what is their LCM?

Solution:

Given: GCF = 18 and product of numbers = 1620
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1620/18
Therefore, the LCM is 90.
Example 3: Find the GCF of 18 and 90, if their LCM is 90.

Solution:

∵ LCM × GCF = 18 × 90
⇒ GCF(18, 90) = (18 × 90)/90 = 18
Therefore, the greatest common factor of 18 and 90 is 18.

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FAQs on GCF of 18 and 90

What is the GCF of 18 and 90?

The GCF of 18 and 90 is 18. To calculate the GCF of 18 and 90, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90) and choose the greatest factor that exactly divides both 18 and 90, i.e., 18.

How to Find the GCF of 18 and 90 by Prime Factorization?

To find the GCF of 18 and 90, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 90 = 2 × 3 × 3 × 5.
⇒ Since 2, 3, 3 are common terms in the prime factorization of 18 and 90. Hence, GCF(18, 90) = 2 × 3 × 3 = 18
☛ Prime Numbers

How to Find the GCF of 18 and 90 by Long Division Method?

To find the GCF of 18, 90 using long division method, 90 is divided by 18. The corresponding divisor (18) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 18, 90?

The following equation can be used to express the relation between LCM and GCF of 18 and 90, i.e. GCF × LCM = 18 × 90.

If the GCF of 90 and 18 is 18, Find its LCM.

GCF(90, 18) × LCM(90, 18) = 90 × 18
Since the GCF of 90 and 18 = 18
⇒ 18 × LCM(90, 18) = 1620
Therefore, LCM = 90
☛ GCF Calculator

What are the Methods to Find GCF of 18 and 90?

There are three commonly used methods to find the GCF of 18 and 90.

By Listing Common Factors
By Long Division
By Prime Factorization

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