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GCF of 15 and 27

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

1.	GCF of 15 and 27
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 27?

Answer: GCF of 15 and 27 is 3.

Explanation:

The GCF of two non-zero integers, x(15) and y(27), is the greatest positive integer m(3) that divides both x(15) and y(27) without any remainder.

Methods to Find GCF of 15 and 27

Let's look at the different methods for finding the GCF of 15 and 27.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 15 and 27 by Long Division

GCF of 15 and 27 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 27 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 15 and 27.

GCF of 15 and 27 by Listing Common Factors

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

There are 2 common factors of 15 and 27, that are 1 and 3. Therefore, the greatest common factor of 15 and 27 is 3.

GCF of 15 and 27 by Prime Factorization

Prime factorization of 15 and 27 is (3 × 5) and (3 × 3 × 3) respectively. As visible, 15 and 27 have only one common prime factor i.e. 3. Hence, the GCF of 15 and 27 is 3.

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GCF of 15 and 27 Examples

Example 1: The product of two numbers is 405. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 405
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 405/3
Therefore, the LCM is 135.
Example 2: Find the GCF of 15 and 27, if their LCM is 135.

Solution:

∵ LCM × GCF = 15 × 27
⇒ GCF(15, 27) = (15 × 27)/135 = 3
Therefore, the greatest common factor of 15 and 27 is 3.
Example 3: Find the greatest number that divides 15 and 27 exactly.

Solution:

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

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FAQs on GCF of 15 and 27

What is the GCF of 15 and 27?

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

How to Find the GCF of 15 and 27 by Prime Factorization?

To find the GCF of 15 and 27, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 27 = 3 × 3 × 3.
⇒ Since 3 is the only common prime factor of 15 and 27. Hence, GCF (15, 27) = 3.
☛ Prime Numbers

If the GCF of 27 and 15 is 3, Find its LCM.

GCF(27, 15) × LCM(27, 15) = 27 × 15
Since the GCF of 27 and 15 = 3
⇒ 3 × LCM(27, 15) = 405
Therefore, LCM = 135
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 15, 27?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 15 and 27, i.e. GCF × LCM = 15 × 27.

How to Find the GCF of 15 and 27 by Long Division Method?

To find the GCF of 15, 27 using long division method, 27 is divided by 15. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 15 and 27?

There are three commonly used methods to find the GCF of 15 and 27.

By Listing Common Factors
By Prime Factorization
By Long Division

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