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GCF of 13 and 39

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

1.	GCF of 13 and 39
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 13 and 39?

Answer: GCF of 13 and 39 is 13.

Explanation:

The GCF of two non-zero integers, x(13) and y(39), is the greatest positive integer m(13) that divides both x(13) and y(39) without any remainder.

Methods to Find GCF of 13 and 39

Let's look at the different methods for finding the GCF of 13 and 39.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 13 and 39 by Listing Common Factors

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

There are 2 common factors of 13 and 39, that are 1 and 13. Therefore, the greatest common factor of 13 and 39 is 13.

GCF of 13 and 39 by Long Division

GCF of 13 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 13 (smaller number).
Step 2: Since the remainder = 0, the divisor (13) is the GCF of 13 and 39.

The corresponding divisor (13) is the GCF of 13 and 39.

GCF of 13 and 39 by Prime Factorization

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

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GCF of 13 and 39 Examples

Example 1: Find the GCF of 13 and 39, if their LCM is 39.

Solution:

∵ LCM × GCF = 13 × 39
⇒ GCF(13, 39) = (13 × 39)/39 = 13
Therefore, the greatest common factor of 13 and 39 is 13.
Example 2: Find the greatest number that divides 13 and 39 exactly.

Solution:

The greatest number that divides 13 and 39 exactly is their greatest common factor, i.e. GCF of 13 and 39.
⇒ Factors of 13 and 39:
- Factors of 13 = 1, 13
- Factors of 39 = 1, 3, 13, 39
Therefore, the GCF of 13 and 39 is 13.
Example 3: The product of two numbers is 507. If their GCF is 13, what is their LCM?

Solution:

Given: GCF = 13 and product of numbers = 507
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 507/13
Therefore, the LCM is 39.

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FAQs on GCF of 13 and 39

What is the GCF of 13 and 39?

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

What are the Methods to Find GCF of 13 and 39?

There are three commonly used methods to find the GCF of 13 and 39.

By Long Division
By Prime Factorization
By Listing Common Factors

What is the Relation Between LCM and GCF of 13, 39?

The following equation can be used to express the relation between LCM and GCF of 13 and 39, i.e. GCF × LCM = 13 × 39.

How to Find the GCF of 13 and 39 by Long Division Method?

To find the GCF of 13, 39 using long division method, 39 is divided by 13. The corresponding divisor (13) when remainder equals 0 is taken as GCF.

If the GCF of 39 and 13 is 13, Find its LCM.

GCF(39, 13) × LCM(39, 13) = 39 × 13
Since the GCF of 39 and 13 = 13
⇒ 13 × LCM(39, 13) = 507
Therefore, LCM = 39
☛ Greatest Common Factor Calculator

How to Find the GCF of 13 and 39 by Prime Factorization?

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

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