GCF of 12 and 27 | How to Find GCF of 12, 27? (2024)

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

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.

☛ Also Check:

GCF of 10 and 45 = 5
GCF of 28 and 36 = 4
GCF of 21 and 36 = 3
GCF of 56 and 49 = 7
GCF of 15 and 30 = 15
GCF of 210 and 90 = 30
GCF of 49 and 98 = 49

GCF of 12 and 27 Examples

Example 1: The product of two numbers is 324. If their GCF is 3, what is their LCM?
See Also
GCF of 32 and 72 | How to Find GCF of 32, 72?
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
☛ Greatest Common Factor Calculator

FAQs

GCF of 12 and 27 | How to Find GCF of 12, 27? ›

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.

Read On ›

What is the greatest common factor GCF of 27 and 27? ›

When you compare the two lists of factors, you can see that the common factor(s) are 1, 3, 9, 27. Since 27 is the largest of these common factors, the GCF of 27 and 27 would be 27.

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Is 12 a factor of 27? ›

27÷8=3 and remainder is 3, Hence 8 is the not factor of 27. 27÷9=3 and remainder is 0, Hence 9 is the factor of 27. 27÷10=2 and remainder is 7, Hence 10 is not the factor of 27. 27÷12=2 and remainder is 3, Hence 12 is not the factor of 27.

How to calculate GCF? ›

The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number. 18 and 24 share one 2 and one 3 in common. We multiply them to get the GCF, so 2 * 3 = 6 is the GCF of 18 and 24.

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What is a multiple of 12 and 27? ›

LCM of 12 and 27 by Listing Multiples

Step 1: List a few multiples of 12 (12, 24, 36, 48, . . . ) and 27 (27, 54, 81, 108, 135, 162, . . . . ) Step 2: The common multiples from the multiples of 12 and 27 are 108, 216, . . . Step 3: The smallest common multiple of 12 and 27 is 108.

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What is the GCF factor of 12? ›

Factors of the number 12: You can evenly divide 12 by 1, 2, 3, 4, 6 and 12. Therefore, we can say that 1,2,3,4,6 and 12 are factors of 12. We can also say that the greatest or largest factor of 12 is 12.

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What are the three methods for finding GCF? ›

To calculate GCF, there are three common ways- division, multiplication, and prime factorization.

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What is the least to greatest factor of 27? ›

Factors of 27 = 1, 3, 9 and 27. Thus, the common factor of 27 and 28 is 1. Example 3: Find the common factors of 27 and 20.

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What is the LCM of 12 and 27? ›

LCM of 12 and 27 is 108. The number divisible by the given two numbers exactly provides the LCM value.

Does 12 have 2 factors? ›

As 12 is an even composite number, it has many factors other than 1 and 12. The factors of 12 can be positive or negative. Hence, the factors of 12 are 1, 2, 3, 4, 6 and 12.

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How to find the GCF quickly? ›

Here's how to find the GCF of a set of numbers using prime factorization:

List the prime factors of each number.
Circle every common prime factor — that is, every prime factor that's a factor of every number in the set.
Multiply all the circled numbers. The result is the GCF.

Jul 9, 2021

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What is the GCF of 27? ›

The factors of 27 are 1, 3, 9, 27. The common factors of 18 and 27 are 1, 3 and 9. The greatest common factor of 18 and 27 is 9.

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Can you find GCF on calculator? ›

A calculator is particularly useful when you need to find the GCF of large numbers. Find the GCF of 504 and 3,150. The GCF is also known as the greatest common divisor, or GCD. The GCD function is found on the MATH menu.

Get More Info Here ›

What is 12 and 7 GCF? ›

What is the GCF of 7 and 12? The GCF of 7 and 12 is 1. To calculate the greatest common factor (GCF) of 7 and 12, we need to factor each number (factors of 7 = 1, 7; factors of 12 = 1, 2, 3, 4, 6, 12) and choose the greatest factor that exactly divides both 7 and 12, i.e., 1.

Do 12 and 25 have a GCF? ›

To find the GCF of 12 and 25, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 25 = 5 × 5. ⇒ There is no common prime factor for 12 and 25. Hence, GCF (12, 25) = 1.

How to find the gcd? ›

Step 1: Find the product of a and b. Step 2: Find the Least Common Multiple (LCM) of a and b. Step 3: Divide the product of the numbers by the LCM of the numbers. Step 4: The obtained value after division is the greatest common divisor of (a, b).

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