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GCF of 39 and 65

GCF of 39 and 65 is the largest possible number that divides 39 and 65 exactly without any remainder. The factors of 39 and 65 are 1, 3, 13, 39 and 1, 5, 13, 65 respectively. There are 3 commonly used methods to find the GCF of 39 and 65 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 39 and 65
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 39 and 65?

Answer: GCF of 39 and 65 is 13.

Explanation:

The GCF of two non-zero integers, x(39) and y(65), is the greatest positive integer m(13) that divides both x(39) and y(65) without any remainder.

Methods to Find GCF of 39 and 65

The methods to find the GCF of 39 and 65 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 39 and 65 by Prime Factorization

Prime factorization of 39 and 65 is (3 × 13) and (5 × 13) respectively. As visible, 39 and 65 have only one common prime factor i.e. 13. Hence, the GCF of 39 and 65 is 13.

GCF of 39 and 65 by Long Division

GCF of 39 and 65 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 65 (larger number) by 39 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (39) by the remainder (26).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (13) is the GCF of 39 and 65.

GCF of 39 and 65 by Listing Common Factors

Factors of 39: 1, 3, 13, 39
Factors of 65: 1, 5, 13, 65

There are 2 common factors of 39 and 65, that are 1 and 13. Therefore, the greatest common factor of 39 and 65 is 13.

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GCF of 39 and 65 Examples

Example 1: Find the greatest number that divides 39 and 65 exactly.

Solution:

The greatest number that divides 39 and 65 exactly is their greatest common factor, i.e. GCF of 39 and 65.
⇒ Factors of 39 and 65:
- Factors of 39 = 1, 3, 13, 39
- Factors of 65 = 1, 5, 13, 65
Therefore, the GCF of 39 and 65 is 13.
Example 2: Find the GCF of 39 and 65, if their LCM is 195.

Solution:

∵ LCM × GCF = 39 × 65
⇒ GCF(39, 65) = (39 × 65)/195 = 13
Therefore, the greatest common factor of 39 and 65 is 13.
Example 3: For two numbers, GCF = 13 and LCM = 195. If one number is 65, find the other number.

Solution:

Given: GCF (y, 65) = 13 and LCM (y, 65) = 195
∵ GCF × LCM = 65 × (y)
⇒ y = (GCF × LCM)/65
⇒ y = (13 × 195)/65
⇒ y = 39
Therefore, the other number is 39.

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FAQs on GCF of 39 and 65

What is the GCF of 39 and 65?

The GCF of 39 and 65 is 13. To calculate the greatest common factor of 39 and 65, we need to factor each number (factors of 39 = 1, 3, 13, 39; factors of 65 = 1, 5, 13, 65) and choose the greatest factor that exactly divides both 39 and 65, i.e., 13.

What are the Methods to Find GCF of 39 and 65?

There are three commonly used methods to find the GCF of 39 and 65.

By Listing Common Factors
By Long Division
By Prime Factorization

What is the Relation Between LCM and GCF of 39, 65?

The following equation can be used to express the relation between LCM and GCF of 39 and 65, i.e. GCF × LCM = 39 × 65.

How to Find the GCF of 39 and 65 by Long Division Method?

To find the GCF of 39, 65 using long division method, 65 is divided by 39. The corresponding divisor (13) when remainder equals 0 is taken as GCF.

If the GCF of 65 and 39 is 13, Find its LCM.

GCF(65, 39) × LCM(65, 39) = 65 × 39
Since the GCF of 65 and 39 = 13
⇒ 13 × LCM(65, 39) = 2535
Therefore, LCM = 195
☛ Greatest Common Factor Calculator

How to Find the GCF of 39 and 65 by Prime Factorization?

To find the GCF of 39 and 65, we will find the prime factorization of the given numbers, i.e. 39 = 3 × 13; 65 = 5 × 13.
⇒ Since 13 is the only common prime factor of 39 and 65. Hence, GCF (39, 65) = 13.
☛ What are Prime Numbers?

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