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GCF of 90 and 135

GCF of 90 and 135 is the largest possible number that divides 90 and 135 exactly without any remainder. The factors of 90 and 135 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 and 1, 3, 5, 9, 15, 27, 45, 135 respectively. There are 3 commonly used methods to find the GCF of 90 and 135 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 90 and 135
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 90 and 135?

Answer: GCF of 90 and 135 is 45.

Explanation:

The GCF of two non-zero integers, x(90) and y(135), is the greatest positive integer m(45) that divides both x(90) and y(135) without any remainder.

Methods to Find GCF of 90 and 135

Let's look at the different methods for finding the GCF of 90 and 135.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 90 and 135 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 = 135 and Y = 90

GCF(135, 90) = GCF(90, 135 mod 90) = GCF(90, 45)
GCF(90, 45) = GCF(45, 90 mod 45) = GCF(45, 0)
GCF(45, 0) = 45 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 90 and 135 is 45.

GCF of 90 and 135 by Long Division

GCF of 90 and 135 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 135 (larger number) by 90 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (90) by the remainder (45).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (45) is the GCF of 90 and 135.

GCF of 90 and 135 by Listing Common Factors

Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135

There are 6 common factors of 90 and 135, that are 1, 3, 5, 9, 45, and 15. Therefore, the greatest common factor of 90 and 135 is 45.

☛ Also Check:

GCF of 90 and 135 Examples

Example 1: Find the GCF of 90 and 135, if their LCM is 270.

Solution:

∵ LCM × GCF = 90 × 135
⇒ GCF(90, 135) = (90 × 135)/270 = 45
Therefore, the greatest common factor of 90 and 135 is 45.
Example 2: For two numbers, GCF = 45 and LCM = 270. If one number is 135, find the other number.

Solution:

Given: GCF (z, 135) = 45 and LCM (z, 135) = 270
∵ GCF × LCM = 135 × (z)
⇒ z = (GCF × LCM)/135
⇒ z = (45 × 270)/135
⇒ z = 90
Therefore, the other number is 90.
Example 3: Find the greatest number that divides 90 and 135 exactly.

Solution:

The greatest number that divides 90 and 135 exactly is their greatest common factor, i.e. GCF of 90 and 135.
⇒ Factors of 90 and 135:
- Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
- Factors of 135 = 1, 3, 5, 9, 15, 27, 45, 135
Therefore, the GCF of 90 and 135 is 45.

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FAQs on GCF of 90 and 135

What is the GCF of 90 and 135?

The GCF of 90 and 135 is 45. To calculate the greatest common factor (GCF) of 90 and 135, we need to factor each number (factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90; factors of 135 = 1, 3, 5, 9, 15, 27, 45, 135) and choose the greatest factor that exactly divides both 90 and 135, i.e., 45.

How to Find the GCF of 90 and 135 by Long Division Method?

To find the GCF of 90, 135 using long division method, 135 is divided by 90. The corresponding divisor (45) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 90, 135?

The following equation can be used to express the relation between Least Common Multiple and GCF of 90 and 135, i.e. GCF × LCM = 90 × 135.

How to Find the GCF of 90 and 135 by Prime Factorization?

To find the GCF of 90 and 135, we will find the prime factorization of the given numbers, i.e. 90 = 2 × 3 × 3 × 5; 135 = 3 × 3 × 3 × 5.
⇒ Since 3, 3, 5 are common terms in the prime factorization of 90 and 135. Hence, GCF(90, 135) = 3 × 3 × 5 = 45
☛ What are Prime Numbers?

If the GCF of 135 and 90 is 45, Find its LCM.

GCF(135, 90) × LCM(135, 90) = 135 × 90
Since the GCF of 135 and 90 = 45
⇒ 45 × LCM(135, 90) = 12150
Therefore, LCM = 270
☛ GCF Calculator

What are the Methods to Find GCF of 90 and 135?

There are three commonly used methods to find the GCF of 90 and 135.

By Long Division
By Euclidean Algorithm
By Prime Factorization

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