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GCF of 12 and 27

GCF of 12 and 27 is the largest possible number that divides 12 and 27 exactly without any remainder. The factors of 12 and 27 are 1, 2, 3, 4, 6, 12 and 1, 3, 9, 27 respectively. There are 3 commonly used methods to find the GCF of 12 and 27 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 12 and 27
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 27?

Answer: GCF of 12 and 27 is 3.

Explanation:

The GCF of two non-zero integers, x(12) and y(27), is the greatest positive integer m(3) that divides both x(12) and y(27) without any remainder.

Methods to Find GCF of 12 and 27

The methods to find the GCF of 12 and 27 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 12 and 27 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 27: 1, 3, 9, 27

There are 2 common factors of 12 and 27, that are 1 and 3. Therefore, the greatest common factor of 12 and 27 is 3.

GCF of 12 and 27 by Prime Factorization

Prime factorization of 12 and 27 is (2 × 2 × 3) and (3 × 3 × 3) respectively. As visible, 12 and 27 have only one common prime factor i.e. 3. Hence, the GCF of 12 and 27 is 3.

GCF of 12 and 27 by Long Division

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

The corresponding divisor (3) is the GCF of 12 and 27.

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GCF of 12 and 27 Examples

Example 1: The product of two numbers is 324. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 324
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 324/3
Therefore, the LCM is 108.
Example 2: Find the greatest number that divides 12 and 27 exactly.

Solution:

The greatest number that divides 12 and 27 exactly is their greatest common factor, i.e. GCF of 12 and 27.
⇒ Factors of 12 and 27:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 27 = 1, 3, 9, 27
Therefore, the GCF of 12 and 27 is 3.
Example 3: Find the GCF of 12 and 27, if their LCM is 108.

Solution:

∵ LCM × GCF = 12 × 27
⇒ GCF(12, 27) = (12 × 27)/108 = 3
Therefore, the greatest common factor of 12 and 27 is 3.

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FAQs on GCF of 12 and 27

What is the GCF of 12 and 27?

The GCF of 12 and 27 is 3. To calculate the greatest common factor of 12 and 27, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 27 = 1, 3, 9, 27) and choose the greatest factor that exactly divides both 12 and 27, i.e., 3.

What are the Methods to Find GCF of 12 and 27?

There are three commonly used methods to find the GCF of 12 and 27.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the GCF of 12 and 27 by Prime Factorization?

To find the GCF of 12 and 27, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 27 = 3 × 3 × 3.
⇒ Since 3 is the only common prime factor of 12 and 27. Hence, GCF (12, 27) = 3.
☛ What is a Prime Number?

How to Find the GCF of 12 and 27 by Long Division Method?

To find the GCF of 12, 27 using long division method, 27 is divided by 12. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 12, 27?

The following equation can be used to express the relation between LCM and GCF of 12 and 27, i.e. GCF × LCM = 12 × 27.

If the GCF of 27 and 12 is 3, Find its LCM.

GCF(27, 12) × LCM(27, 12) = 27 × 12
Since the GCF of 27 and 12 = 3
⇒ 3 × LCM(27, 12) = 324
Therefore, LCM = 108
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