65 of what number is 39

The first step to this method of finding the Least Common Multiple of 39 and 65 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number.

Let’s take a look at the multiples for each of these numbers, 39 and 65:

What are the Multiples of 39?

What are the Multiples of 65?

Let’s take a look at the first 10 multiples for each of these numbers, 39 and 65:

First 10 Multiples of 39: 39, 78, 117, 156, 195, 234, 273, 312, 351, 390

First 10 Multiples of 65: 65, 130, 195, 260, 325, 390, 455, 520, 585, 650

You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 39 and 65 are 195, 390, 585. Because 195 is the smallest, it is the least common multiple.

The LCM of 39 and 65 is 195.

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.

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.

☛ Also Check:

• GCF of 64 and 120 = 8
• GCF of 22 and 44 = 22
• GCF of 36 and 40 = 4
• GCF of 56 and 84 = 28
• GCF of 56 and 35 = 7
• GCF of 30 and 40 = 10
• GCF of 28 and 36 = 4

GCF of 39 and 65 Examples

1. 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.

2. 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.

3. 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.

Show Solution >

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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.
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