## A Simple Example of How to Find Factors in Algebra

Finding the factors of a term is easy. Find the factors of any numbers and of each letter and bracket that appears in the term.## Question

What are the factors of the term shown below?## Step-by-Step:

## 1

## 2

Find each letter or bracket that appears in the term.
In our example,

**x**is the only letter.## 3

The term itself is also a factor. In our example,

**2x**is the term.## Answer:

The factors of**2x**are:

## A More Complicated Example of How to Find Factors in Algebra

Things get more complicated when there are exponents and brackets.## Question

What are the factors of the term shown below?## Step-by-Step:

## 1

Find the factors of the number. In our example, the number is 4.
The factors of

**4**are**1**,**2**and**4**.## 2

Find each letter or bracket that appears in the term, being careful of any exponents.

- The first letter is
**x**. It has an exponent (or power) of 2 (x squared). When there is an exponent with a letter, we need to include every power of that letter up to and including that exponent.**x**and**x**are factors.^{2} - The only bracket is
**(y + 1)**.**(y + 1)**is a factor.

## 3

The term itself is also a factor. In our example,

**4x**is the term.^{2}(y + 1)## Answer:

The factors of**4x**are:

^{2}(y + 1)## Products of Factors Are Also (Usually) Factors

While**1**,

**2**,

**4**,

**x**,

**x**,

^{2}**y + 1**and

**4x**are all factors of

^{2}(y + 1)**4x**, they are not the only factors. Other factors can be found by multiplying these factors together. For example,

^{2}(y + 1)**2**and**x**are factors, so**2x**is also a factor.**4**,**x**and**y + 1**are factors, so**4x(y + 1)**is also a factor.

**2**and**4**are both factors, but their product**8**can not be a factor. Any product of number factors greater than the actual number in the term (4 in our example) can not be a factor.**x**and**x**are both factors, but their product^{2}**x**can not be a factor. Any product of letters can not have an exponent greater than the exponent of the letter in the term (x^{3}^{2}in our example).**4x**is the both a factor of the term and the term itself. It can not be multiplied by another other factor (apart from 1) to make another factor.^{2}(y + 1)

## What Is a Factor in Algebra?

A factor is a quantity that divides exactly into a term. A factor is one of the numbers, letters and brackets (or a product of them) that are multiplied together to make a term.## Numbers Have Factors

A factor is a number which divides exactly into another number. For example, the factors of**4**are

**1**,

**2**and

**4**because they all divide exactly in 4. If an term in algebra includes a number, the factors of the number are also factors of the term. For example. the factors of

**4xy**are

**1**,

**2**,

**4**,

**x**and

**y**.

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