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

The **factors of X** are numbers that when divided by X leave zero as the remainder. This means the numbers that completely divide the given number are named as its factors. The factors of the given number can be positive as well as negative provided that the given number is achieved upon multiplication of two-factor integers.

### Factors of X

Here are the factors of number** X.**

**Factors of X**: a, b, c, X

### Negative Factors of X

The **negative factors of X** are similar to its positive factors, just with a negative sign.

**Negative Factors of X**: -a, -b, -c, and -X

### Prime Factorization of X

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

**Prime Factorization**: a x b

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

## What Are the Factors of X?

**The factors of X are a, b, c, and X. All of these numbers are the factors as they do not leave any remainder when divided by X.**

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

## How To Find the Factors of X?

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

\[\dfrac{X}{1} = X\]

\[\dfrac{X}{a} = d\]

\[\dfrac{X}{b} = e\]

\[\dfrac{X}{X} = 1\]

Therefore, a, b, c, and X are the factors of X.

### Total Number of Factors of X

For X there are n** positive factors** and n** negative** ones. So in total, there are m factors of X.

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

- Find the factorization/prime factorization of the given number.
- Demonstrate the prime factorization of the number in the form of exponent form.
- Add 1 to each of the exponents of the prime factor.
- 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 X is given as:

Factorization of X is** a x b x c**.

The exponent of a, b, and c is k.

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

Therefore, the **total number of factors** of X is m. n are positive and n factors are negative.

### Important Notes

Here are some important 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 X by Prime Factorization

The **number X** is a composite/prime number. Prime factorization is a useful technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of X 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 X, start dividing by its **smallest 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 X** can be expressed as:

**X = a x b**

## Factors of X 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 of the given numbers.

For X, the factor pairs can be found as:

**1 x X = X**

**a x b = X **

The possible** factor pairs of X **are given as **(1, X) **and **(a, b )**.

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

The **negative factor pairs** of X are given as:

**-1 x -X = X **

**-a x -b = X**

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, -a, -b, -c, and -X are called negative factors of X.

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

**Factor list of X: a, -a, b, -b, c, -c, X, and -X**

## Factors of X Solved Examples

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

### Example 1

How many factors of X are there?

### Solution

The total number of Factors of X is m.

Factors of X are a, b, c, and X.

### Example 2

Find the factors of X using prime factorization.

### Solution

The prime factorization of X is given as:

\[ X \div a = v \]

\[ v \div v = 1 \]

So the prime factorization of X can be written as:

**a x b = X**