A day full of math games & activities. Find one near you.

GCF of 6 and 27

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

1.	GCF of 6 and 27
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 6 and 27?

Answer: GCF of 6 and 27 is 3.

Explanation:

The GCF of two non-zero integers, x(6) and y(27), is the greatest positive integer m(3) that divides both x(6) and y(27) without any remainder.

Methods to Find GCF of 6 and 27

Let's look at the different methods for finding the GCF of 6 and 27.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 6 and 27 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 = 27 and Y = 6

GCF(27, 6) = GCF(6, 27 mod 6) = GCF(6, 3)
GCF(6, 3) = GCF(3, 6 mod 3) = GCF(3, 0)
GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 6 and 27 is 3.

GCF of 6 and 27 by Long Division

GCF of 6 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 6 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (6) by the remainder (3).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 6 and 27.

GCF of 6 and 27 by Prime Factorization

Prime factorization of 6 and 27 is (2 × 3) and (3 × 3 × 3) respectively. As visible, 6 and 27 have only one common prime factor i.e. 3. Hence, the GCF of 6 and 27 is 3.

☛ Also Check:

GCF of 6 and 27 Examples

Example 1: Find the greatest number that divides 6 and 27 exactly.

Solution:

The greatest number that divides 6 and 27 exactly is their greatest common factor, i.e. GCF of 6 and 27.
⇒ Factors of 6 and 27:
- Factors of 6 = 1, 2, 3, 6
- Factors of 27 = 1, 3, 9, 27
Therefore, the GCF of 6 and 27 is 3.
Example 2: The product of two numbers is 162. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 162
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 162/3
Therefore, the LCM is 54.
Example 3: For two numbers, GCF = 3 and LCM = 54. If one number is 27, find the other number.

Solution:

Given: GCF (x, 27) = 3 and LCM (x, 27) = 54
∵ GCF × LCM = 27 × (x)
⇒ x = (GCF × LCM)/27
⇒ x = (3 × 54)/27
⇒ x = 6
Therefore, the other number is 6.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 6 and 27

What is the GCF of 6 and 27?

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

What are the Methods to Find GCF of 6 and 27?

There are three commonly used methods to find the GCF of 6 and 27.

By Long Division
By Prime Factorization
By Listing Common Factors

What is the Relation Between LCM and GCF of 6, 27?

The following equation can be used to express the relation between LCM and GCF of 6 and 27, i.e. GCF × LCM = 6 × 27.

How to Find the GCF of 6 and 27 by Prime Factorization?

To find the GCF of 6 and 27, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 27 = 3 × 3 × 3.
⇒ Since 3 is the only common prime factor of 6 and 27. Hence, GCF (6, 27) = 3.
☛ Prime Number

How to Find the GCF of 6 and 27 by Long Division Method?

To find the GCF of 6, 27 using long division method, 27 is divided by 6. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

If the GCF of 27 and 6 is 3, Find its LCM.

GCF(27, 6) × LCM(27, 6) = 27 × 6
Since the GCF of 27 and 6 = 3
⇒ 3 × LCM(27, 6) = 162
Therefore, LCM = 54
☛ Greatest Common Factor Calculator

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum