 # Factors of 393: Prime Factorization, Methods, and Examples

A number’s factors are a set of numbers that the number can be divided evenly into. For example, 393 is not a prime number and has 8 factors. Factors can also be thought of as building blocks. These two elements are multiplied to get the resultant number.

### Factors of 393

Here are the factors of number 393.

Factors of 393: 1, 3, 131 and 393

### Negative Factors of 393

The negative factors of 393 are similar to their positive aspects, just with a negative sign.

Negative Factors of 393: -1, -3, -131 and -393

### Prime Factorization of 393

The prime factorization of 393 is the way of expressing its prime factors in the product form.

Prime Factorization:  3 X 131

In this article, we will learn about the factors of 393 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 393?

The factors of 393 are 1, 3, 131, and 393. These numbers are the factors as they do not leave any remainder when divided by 393.

The factors of 393 are classified as prime numbers and composite numbers. The prime factors of the number 393 can be determined using the prime factorization technique.

## How To Find the Factors of 393?

You can find the factors of 393 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 393, create a list containing the numbers that are exactly divisible by 393 with zero remainders. One important thing to note is that 1 and 393 are the 393’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 393 are determined as follows:

$\dfrac{393}{1} = 393$

$\dfrac{393}{3} = 131$

$\dfrac{393}{131} = 3$

$\dfrac{393}{393} = 1$

Therefore, 1, 3, 131, and 393 are the factors of 393.

### Total Number of Factors of 393

For 393, there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 393.

To find the total number of factors of the given number, follow the procedure mentioned below:

1. Find the factorization/prime factorization of the given number.
2. Demonstrate the prime factorization of the number in the form of exponent form.
3. Add 1 to each of the exponents of the prime factor.
4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of 393 is given as:

Factorization of 393 is 1, 3, 131, and 393.

The exponent of 1, 3, 131, and 393 is 1.

Adding 1 to each and multiplying them together results in 8.

Therefore, the total number of factors of 393 is 8. 4 is positive, and 4 factors are negative.

### Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

• The factor of any given number must be a whole number.
• The factors of the number cannot be in the form of decimals or fractions.
• Factors can be positive as well as negative.
• Negative factors are the additive inverse of the positive factors of a given number.
• The factor of a number cannot be greater than that number.
• Every even number has 2 as its prime factor, the smallest prime factor.

## Factors of 393 by Prime Factorization

The number 393 is a composite number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors. Before finding the factors of 393 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 393, divide by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 393 can be expressed as:

393 = 3 X 131

## Factors of 393 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors. For 393, the factor pairs can be found as:

1 x 393 = 393

3 X 131 = 393

The possible factor pairs of  393 are given as (1, 393) and (3, 393).

All these numbers in pairs, when multiplied, give 393 as the product.

The negative factor pairs of 393 are given as:

-1 x -393 = 393

-3 X -131 = -393

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -3, -131, and -393 are negative factors of 393.

The list of all the factors of 393, including positive and negative numbers, is given below.

Factor list of 393:1,-1, 3,-3,131, -131  393, and -393

## Factors of 393 Solved Examples

To better understand the concept of factors, let’s solve some examples.

### Example 1

How many factors of 393 are there?

### Solution

The total number of Factors of 393 is 8.

Factors of 393 are 1, 3, 131, and 393.

### Example 2

Find the factors of 393 using prime factorization.

### Solution

The prime factorization of 393 is given as:

393 $\div$ 3 = 131

131 $\div$ 131 = 1

So the prime factorization of 393 can be written as:

3 X 131= 393