 # Factors of 909: Prime Factorization, Methods, and Examples

1, 3, 9, 101, 303 and 909 make up 909. The integers divisible by the specified number are the factors. The odd composite number 909 has four components. .

### Factors of 909

Here are the factors of number 909.

Factors of 909: 1, 3, 9, 101, 303 and 909

### Negative Factors of 909

The negative factors of 909 are similar to their positive aspects, just with a negative sign.

Negative Factors of 909: -1, -3, -9, -101, -303 and -909

### Prime Factorization of 909

The prime factorization of 909 is the way of expressing its prime factors in the product form.

Prime Factorization: 32 x 1011

In this article, we will learn about the factors of 909 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 909?

The factors of 909 are 1, 3, 9, 101, 303 and 909. These numbers are the factors as they do not leave any remainder when divided by 909.

The factors of 909 are classified as prime numbers and composite numbers. The prime factors of the number 909 can be determined using the prime factorization technique.

## How To Find the Factors of 909?

You can find the factors of 909 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 909, create a list containing the numbers that are exactly divisible by 909 with zero remainders. One important thing to note is that 1 and 909 are the 909’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 909 are determined as follows:

$\dfrac{909}{1} = 909$

$\dfrac{909}{3} = 303$

$\dfrac{909}{9} = 101$

$\dfrac{909}{101} = 9$

$\dfrac{909}{303} =3$

$\dfrac{909}{909} = 1$

Therefore, 1, 3, 9, 101, 303 and 909 are the factors of 909.

### Total Number of Factors of 909

For 909, there are 6 positive factors and 6 negative ones. So in total, there are 12 factors out of 909.

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 909 is given as:

Factorization of 909 is 1 x 32 x 1011 .

The exponent of 1 is 1, 3 is 2, and 101 is 1.

Adding 1 to each and multiplying them together results in 12.

Therefore, the total number of factors 909 is 12. 6 are positive, and 6 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 909 by Prime Factorization  The number 909 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 909 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 909, start dividing 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 909 can be expressed as:

909 = 32 x 1011

## Factors of 909 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 given.

For 909, the factor pairs can be found as:

1 x 909 = 909

3 x 303 = 909

9  x 101 = 909

The possible factor pairs of 909 are given as (1, 909), (3, 303), and (9, 101).

All these numbers in pairs, when multiplied, give 909 as the product.

The negative factor pairs of 909 are given as:

-1 x -909 = 909

-3 x -303 = 909

-9  x -101 = 909

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, -9, -101, -303 and -909 are called negative factors of 909.

The list of all the factors of909, including positive as well as negative numbers, is given below.

Factor list of 909: 1,-1, 3,-3, 9,-9, 101,-101, 303,-303, 909, and -909

## Factors of 909 Solved Examples

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

### Example 1

How many factors of 909 are there?

### Solution

The total number of Factors 909 is 12.

Factors of 909 are 1, 3, 9, 101, 303 and 909.

### Example 2

Find the factors of 909 using prime factorization.

### Solution

The prime factorization of 909 is given as:

909 $\div$ 3 = 303

303 $\div$ 3 = 101

101$\div$ 101 = 1

So the prime factorization of 909 can be written as:

32 x 1011 = 909