Factors

# Factors of 39 | Prime Factorization of 39 | Factor Tree of 39

Written by Prerit Jain

Updated on: 12 Aug 2023

### Factors of 39 | Prime Factorization of 39 | Factor Tree of 39

Factors of 39: Factors are the list of numbers that divide another number evenly and do not leave behind a remainder. 39 is a number that has 4 factors in total: 1, 3, 13, and 39 will divide 39 evenly. So, they are considered factors of 39.

The factors of a number can be positive or negative. These factors can also be written in pairs. Multiplying the numbers in a pair will give the original product. In this article, we will discuss how to find factors of 39, its prime factorization, and factor trees with solved examples. To learn more, keep reading.

## What Are the Factors of 39?

The factors of 39 will divide it evenly without leaving any remainder. They can be positive or negative. The table below explains this concept.

## What Are the Factors of 39 in Pairs?

Every number has pair factors, which when multiplied give that particular number (39). They are also written in positive and negative pairs as shown in the tables below:

### Positive Pair Factors of 39

The positive pair factors of 39: (1, 39) and (3, 13).

### Negative Pair Factors of 39

The negative pair factors of 39: (-1, -39) and (-3, -13).

## How To Find Factors of 39 Using the Division Method?

We are using the division method to determine the factors of 39. The division method needs you to multiply a set of sequential natural numbers by 39. The numbers that divide the number 39 completely without leaving any remainder are known as factors of 39. The following are the detailed steps for finding factors of 39 using the division method:

• 39 ÷ 1 = 39
• 39 ÷ 3 = 13
• 39 ÷ 13 = 3
• 39 ÷ 39 = 1

Therefore, we can see that 1, 3, 13, and 39 are the numbers that do not leave any remainder when divided by 39. Hence, the factors of 39 are 1, 3, 13, and 39.

## What Is the Prime Factorization of 39?

First, you need to check if the number given is a prime number or a composite number. If it is a prime number, then it has only two factors: 1 and 39. If it is a composite number, then it has more than two factors.
39 is the composite number. So, it has more than two factors. Hence, we can use the prime factorization method to find the factors of 39.
The steps to find prime factors of 39 using the prime factorization method are given below:

• Step 1: Divide 39 with the smallest prime number that can divide it. The smallest prime number that is divisible by 39 is 3: 39 ÷ 3 = 13
• Step 2: Now, let us attempt to divide the quotient 13, with the smallest prime number. But 13 happens to be a prime number and can only be divided by 1 and 13. Dividing 13 and 13 gives us 1: 13 ÷ 13 = 1
• The quotient is 1. Since 1 cannot be divided further, the prime factors of 39 are 3 X 13. We can also write it down as 3 and 13, as both of them are prime numbers.

Pictorial representation of the prime factorization of 39:

## What is the Factor Tree of 39?

Students can use the factor tree method as well, to find the prime factors of 39. This method instructs us to place the number 39 at the top of the factor tree. As part of its branches, we will note down any set of pair factors of 39. We will, again, split this into a pair of factors. This process will go on till the branches become prime numbers.

• Step 1: Let’s place the number 39 on the top of the factor tree. Now, let’s write down 39 in pairs. We have chosen 3 and 13.
• Step 2: Since 3 and 13 are both prime numbers, we can no longer separate them. The branches in the factor tree will now be all the prime numbers.

Hence, circling all the branches, 3 X 13 = 39, which are 39 prime factors.
There are many ways in which we can write the factor tree of 39. Below is an image representation of the factor tree of 39, choosing 3 and 13 as pair factors of 39.

## Solved Examples on Factors of 39

Here are some solved examples of factors of 39:

What is the sum of all the factors of 39?
1, 3, 13, and 39 are the 39 factors.
1 + 3 + 13 + 39 = 56
Hence, 56 is the sum of all 39 factors.

What are the factors and prime factors of 39?
The factors of 39 are 1, 3, 13, and 39.
The prime factors of 39 are 3 X 13.

What’s the highest common factor between 39 and 52?
The factors of 39 are 1, 3, 13, and 39.
Factors of 52 are 1, 2, 4, 13, 26, and 52.
Hence, from the above, the common factors of 39 and 52 are 1 and 13.
The highest common factor between 39 and 52 is 13.

What’s the highest common factor between 39 and 195?
The factors of 39 are 1, 3, 13, and 39.
The factors of 195 are 1, 3, 5, 13, 15, 39, 65, and 195.
Hence, from the above, the common factors of 39 and 195 are 1, 3, 13, and 39.
The highest common factor between 39 and 195 is 39.

Is 273 a factor of 39?
No, 273 is not a factor of 39.
But 273 is a multiple of 39. A multiple is that which can be divided by another number without leaving any remainder.
As 39 X 7 = 273.

What are the factors of -39?
The factors of -39 are -1, -3, -13 and -39.

What are the common factors of 39 and 65?
To find the common factors of 39 and 65, we need to find the factors of both numbers.
Factors of 39: 1, 3, 13, and 39
Factors of 54: 1, 2, 3, 6, 9, 18, 27, and 54
Hence the common factors of 39 and 65 are 1 and 3.

What are all the factors of 39?
The factors of 39 are 1, 3, 13, and 39.

What are the factors of 39 that are composite?
Any number which has more than 2 factors is known as a composite number. The number which has more than 2 factors in factors of 39 is 39.
So, the composite factor of 39 is 39.

What factors of 39 are multiples of 3?
The factors of 39 that are multiples of 3 are 3 and 39.
3 x 1 = 3
3 x 13 = 39.

How many 39 factors are odd?
All factors of 39 are odd numbers and they are 1, 3, 13, and 39.

What are the factors of 39 and 26?
The factors of 39 are 1, 3, 13, and 39.
The factors of 26 are 1, 2, 13, and 26.

What are the common factors of 39 and 100?
To list out the common factors of 39 and 100, we need to find the factors of both numbers.
Factors of 39: 1, 3, 13 and 39
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100
From the above, the common factor of 39 and 100 is 1.

How many different factors are there for the number 39?
A total of 4 factors are there for the number 39 and they are 1, 3, 13, and 39.

What factors of 39 that are multiples of 3?
The factors of 39 that are multiples of 3 are 3 and 39.

How many pair factors are there in 39?
A total of 2 pairs are there in factors of 39. They are (1, 39); (3, 13).

What is the largest factor of 39?
The largest factor of 39 is 39.
The second largest factor of 39 is 13.

## FAQs on Factors of 39

List all the factors of 39
1, 3, 13, and 39 are the 39 factors.

What are the composite factors of 39?
39 is the only composite factor of 39. Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 39 in pairs?
(1, 39) and (3, 13) are the factors of 39 in pairs.

What are the positive factors for 39?
1, 3, 13, and 39 are the positive factors for 39.

List the first 10 multiples of 39.
Multiples are numbers that can be divided by the given number evenly, without any reminders.
The first 10 multiples of 39 are 39, 78, 117, 156, 195, 234, 273, 312, 351, and 390.

Now, you have learned all about the factors of 39. We hope this blog has proven useful to you and has been easy to understand.

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Prerit Jain

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