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GCF of 90 and 27

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

1.	GCF of 90 and 27
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 90 and 27?

Answer: GCF of 90 and 27 is 9.

Explanation:

The GCF of two non-zero integers, x(90) and y(27), is the greatest positive integer m(9) that divides both x(90) and y(27) without any remainder.

Methods to Find GCF of 90 and 27

Let's look at the different methods for finding the GCF of 90 and 27.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 90 and 27 by Listing Common Factors

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

There are 3 common factors of 90 and 27, that are 1, 3, and 9. Therefore, the greatest common factor of 90 and 27 is 9.

GCF of 90 and 27 by Prime Factorization

Prime factorization of 90 and 27 is (2 × 3 × 3 × 5) and (3 × 3 × 3) respectively. As visible, 90 and 27 have common prime factors. Hence, the GCF of 90 and 27 is 3 × 3 = 9.

GCF of 90 and 27 by Long Division

GCF of 90 and 27 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 90 (larger number) by 27 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (27) by the remainder (9).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (9) is the GCF of 90 and 27.

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GCF of 90 and 27 Examples

Example 1: Find the GCF of 90 and 27, if their LCM is 270.

Solution:

∵ LCM × GCF = 90 × 27
⇒ GCF(90, 27) = (90 × 27)/270 = 9
Therefore, the greatest common factor of 90 and 27 is 9.
Example 2: For two numbers, GCF = 9 and LCM = 270. If one number is 90, find the other number.

Solution:

Given: GCF (y, 90) = 9 and LCM (y, 90) = 270
∵ GCF × LCM = 90 × (y)
⇒ y = (GCF × LCM)/90
⇒ y = (9 × 270)/90
⇒ y = 27
Therefore, the other number is 27.
Example 3: Find the greatest number that divides 90 and 27 exactly.

Solution:

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

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FAQs on GCF of 90 and 27

What is the GCF of 90 and 27?

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

How to Find the GCF of 90 and 27 by Long Division Method?

To find the GCF of 90, 27 using long division method, 90 is divided by 27. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

If the GCF of 27 and 90 is 9, Find its LCM.

GCF(27, 90) × LCM(27, 90) = 27 × 90
Since the GCF of 27 and 90 = 9
⇒ 9 × LCM(27, 90) = 2430
Therefore, LCM = 270
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 90, 27?

The following equation can be used to express the relation between Least Common Multiple and GCF of 90 and 27, i.e. GCF × LCM = 90 × 27.

How to Find the GCF of 90 and 27 by Prime Factorization?

To find the GCF of 90 and 27, we will find the prime factorization of the given numbers, i.e. 90 = 2 × 3 × 3 × 5; 27 = 3 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 90 and 27. Hence, GCF(90, 27) = 3 × 3 = 9
☛ What is a Prime Number?

What are the Methods to Find GCF of 90 and 27?

There are three commonly used methods to find the GCF of 90 and 27.

By Prime Factorization
By Long Division
By Listing Common Factors

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