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GCF of 27 and 45

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

1.	GCF of 27 and 45
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 27 and 45?

Answer: GCF of 27 and 45 is 9.

Explanation:

The GCF of two non-zero integers, x(27) and y(45), is the greatest positive integer m(9) that divides both x(27) and y(45) without any remainder.

Methods to Find GCF of 27 and 45

Let's look at the different methods for finding the GCF of 27 and 45.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 27 and 45 by Long Division

GCF of 27 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 27 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (27) by the remainder (18).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (9) is the GCF of 27 and 45.

GCF of 27 and 45 by Prime Factorization

Prime factorization of 27 and 45 is (3 × 3 × 3) and (3 × 3 × 5) respectively. As visible, 27 and 45 have common prime factors. Hence, the GCF of 27 and 45 is 3 × 3 = 9.

GCF of 27 and 45 by Listing Common Factors

Factors of 27: 1, 3, 9, 27
Factors of 45: 1, 3, 5, 9, 15, 45

There are 3 common factors of 27 and 45, that are 1, 3, and 9. Therefore, the greatest common factor of 27 and 45 is 9.

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GCF of 27 and 45 Examples

Example 1: For two numbers, GCF = 9 and LCM = 135. If one number is 45, find the other number.

Solution:

Given: GCF (x, 45) = 9 and LCM (x, 45) = 135
∵ GCF × LCM = 45 × (x)
⇒ x = (GCF × LCM)/45
⇒ x = (9 × 135)/45
⇒ x = 27
Therefore, the other number is 27.
Example 2: Find the greatest number that divides 27 and 45 exactly.

Solution:

The greatest number that divides 27 and 45 exactly is their greatest common factor, i.e. GCF of 27 and 45.
⇒ Factors of 27 and 45:
- Factors of 27 = 1, 3, 9, 27
- Factors of 45 = 1, 3, 5, 9, 15, 45
Therefore, the GCF of 27 and 45 is 9.
Example 3: Find the GCF of 27 and 45, if their LCM is 135.

Solution:

∵ LCM × GCF = 27 × 45
⇒ GCF(27, 45) = (27 × 45)/135 = 9
Therefore, the greatest common factor of 27 and 45 is 9.

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FAQs on GCF of 27 and 45

What is the GCF of 27 and 45?

The GCF of 27 and 45 is 9. To calculate the GCF (Greatest Common Factor) of 27 and 45, we need to factor each number (factors of 27 = 1, 3, 9, 27; factors of 45 = 1, 3, 5, 9, 15, 45) and choose the greatest factor that exactly divides both 27 and 45, i.e., 9.

If the GCF of 45 and 27 is 9, Find its LCM.

GCF(45, 27) × LCM(45, 27) = 45 × 27
Since the GCF of 45 and 27 = 9
⇒ 9 × LCM(45, 27) = 1215
Therefore, LCM = 135
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How to Find the GCF of 27 and 45 by Prime Factorization?

To find the GCF of 27 and 45, we will find the prime factorization of the given numbers, i.e. 27 = 3 × 3 × 3; 45 = 3 × 3 × 5.
⇒ Since 3, 3 are common terms in the prime factorization of 27 and 45. Hence, GCF(27, 45) = 3 × 3 = 9
☛ What is a Prime Number?

What are the Methods to Find GCF of 27 and 45?

There are three commonly used methods to find the GCF of 27 and 45.

By Listing Common Factors
By Prime Factorization
By Long Division

How to Find the GCF of 27 and 45 by Long Division Method?

To find the GCF of 27, 45 using long division method, 45 is divided by 27. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 27, 45?

The following equation can be used to express the relation between Least Common Multiple and GCF of 27 and 45, i.e. GCF × LCM = 27 × 45.

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