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GCF of 27 and 39

GCF of 27 and 39 is the largest possible number that divides 27 and 39 exactly without any remainder. The factors of 27 and 39 are 1, 3, 9, 27 and 1, 3, 13, 39 respectively. There are 3 commonly used methods to find the GCF of 27 and 39 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 27 and 39
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 27 and 39?

Answer: GCF of 27 and 39 is 3.

Explanation:

The GCF of two non-zero integers, x(27) and y(39), is the greatest positive integer m(3) that divides both x(27) and y(39) without any remainder.

Methods to Find GCF of 27 and 39

Let's look at the different methods for finding the GCF of 27 and 39.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 27 and 39 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 = 39 and Y = 27

GCF(39, 27) = GCF(27, 39 mod 27) = GCF(27, 12)
GCF(27, 12) = GCF(12, 27 mod 12) = GCF(12, 3)
GCF(12, 3) = GCF(3, 12 mod 3) = GCF(3, 0)
GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 27 and 39 is 3.

GCF of 27 and 39 by Long Division

GCF of 27 and 39 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 39 (larger number) by 27 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (27) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 27 and 39.

GCF of 27 and 39 by Listing Common Factors

Factors of 27: 1, 3, 9, 27
Factors of 39: 1, 3, 13, 39

There are 2 common factors of 27 and 39, that are 1 and 3. Therefore, the greatest common factor of 27 and 39 is 3.

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GCF of 27 and 39 Examples

Example 1: Find the greatest number that divides 27 and 39 exactly.

Solution:

The greatest number that divides 27 and 39 exactly is their greatest common factor, i.e. GCF of 27 and 39.
⇒ Factors of 27 and 39:
- Factors of 27 = 1, 3, 9, 27
- Factors of 39 = 1, 3, 13, 39
Therefore, the GCF of 27 and 39 is 3.
Example 2: The product of two numbers is 1053. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 1053
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1053/3
Therefore, the LCM is 351.
Example 3: Find the GCF of 27 and 39, if their LCM is 351.

Solution:

∵ LCM × GCF = 27 × 39
⇒ GCF(27, 39) = (27 × 39)/351 = 3
Therefore, the greatest common factor of 27 and 39 is 3.

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FAQs on GCF of 27 and 39

What is the GCF of 27 and 39?

The GCF of 27 and 39 is 3. To calculate the GCF (Greatest Common Factor) of 27 and 39, we need to factor each number (factors of 27 = 1, 3, 9, 27; factors of 39 = 1, 3, 13, 39) and choose the greatest factor that exactly divides both 27 and 39, i.e., 3.

What is the Relation Between LCM and GCF of 27, 39?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 27 and 39, i.e. GCF × LCM = 27 × 39.

If the GCF of 39 and 27 is 3, Find its LCM.

GCF(39, 27) × LCM(39, 27) = 39 × 27
Since the GCF of 39 and 27 = 3
⇒ 3 × LCM(39, 27) = 1053
Therefore, LCM = 351
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What are the Methods to Find GCF of 27 and 39?

There are three commonly used methods to find the GCF of 27 and 39.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 27 and 39 by Long Division Method?

To find the GCF of 27, 39 using long division method, 39 is divided by 27. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

How to Find the GCF of 27 and 39 by Prime Factorization?

To find the GCF of 27 and 39, we will find the prime factorization of the given numbers, i.e. 27 = 3 × 3 × 3; 39 = 3 × 13.
⇒ Since 3 is the only common prime factor of 27 and 39. Hence, GCF (27, 39) = 3.
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