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GCF of 39 and 6

GCF of 39 and 6 is the largest possible number that divides 39 and 6 exactly without any remainder. The factors of 39 and 6 are 1, 3, 13, 39 and 1, 2, 3, 6 respectively. There are 3 commonly used methods to find the GCF of 39 and 6 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 39 and 6
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 39 and 6?

Answer: GCF of 39 and 6 is 3.

Explanation:

The GCF of two non-zero integers, x(39) and y(6), is the greatest positive integer m(3) that divides both x(39) and y(6) without any remainder.

Methods to Find GCF of 39 and 6

Let's look at the different methods for finding the GCF of 39 and 6.

Listing Common Factors
Using Euclid's Algorithm
Prime Factorization Method

GCF of 39 and 6 by Listing Common Factors

Factors of 39: 1, 3, 13, 39
Factors of 6: 1, 2, 3, 6

There are 2 common factors of 39 and 6, that are 1 and 3. Therefore, the greatest common factor of 39 and 6 is 3.

GCF of 39 and 6 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 = 6

GCF(39, 6) = GCF(6, 39 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 39 and 6 is 3.

GCF of 39 and 6 by Prime Factorization

Prime factorization of 39 and 6 is (3 × 13) and (2 × 3) respectively. As visible, 39 and 6 have only one common prime factor i.e. 3. Hence, the GCF of 39 and 6 is 3.

☛ Also Check:

GCF of 39 and 6 Examples

Example 1: Find the GCF of 39 and 6, if their LCM is 78.

Solution:

∵ LCM × GCF = 39 × 6
⇒ GCF(39, 6) = (39 × 6)/78 = 3
Therefore, the greatest common factor of 39 and 6 is 3.
Example 2: For two numbers, GCF = 3 and LCM = 78. If one number is 6, find the other number.

Solution:

Given: GCF (x, 6) = 3 and LCM (x, 6) = 78
∵ GCF × LCM = 6 × (x)
⇒ x = (GCF × LCM)/6
⇒ x = (3 × 78)/6
⇒ x = 39
Therefore, the other number is 39.
Example 3: The product of two numbers is 234. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 234
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 234/3
Therefore, the LCM is 78.

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FAQs on GCF of 39 and 6

What is the GCF of 39 and 6?

The GCF of 39 and 6 is 3. To calculate the GCF (Greatest Common Factor) of 39 and 6, we need to factor each number (factors of 39 = 1, 3, 13, 39; factors of 6 = 1, 2, 3, 6) and choose the greatest factor that exactly divides both 39 and 6, i.e., 3.

How to Find the GCF of 39 and 6 by Prime Factorization?

To find the GCF of 39 and 6, we will find the prime factorization of the given numbers, i.e. 39 = 3 × 13; 6 = 2 × 3.
⇒ Since 3 is the only common prime factor of 39 and 6. Hence, GCF (39, 6) = 3.
☛ Prime Numbers

How to Find the GCF of 39 and 6 by Long Division Method?

To find the GCF of 39, 6 using long division method, 39 is divided by 6. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 39, 6?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 39 and 6, i.e. GCF × LCM = 39 × 6.

What are the Methods to Find GCF of 39 and 6?

There are three commonly used methods to find the GCF of 39 and 6.

By Long Division
By Prime Factorization
By Listing Common Factors

If the GCF of 6 and 39 is 3, Find its LCM.

GCF(6, 39) × LCM(6, 39) = 6 × 39
Since the GCF of 6 and 39 = 3
⇒ 3 × LCM(6, 39) = 234
Therefore, LCM = 78
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