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# Factors in Algebra

(KS3, Year 7)

## The Lesson

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.## Real Examples of Factors in Algebra

It is easier to understand factors with examples.-
**2**and**x**are factors of**2x**.

**2**and**x**are multiplied together to make**2x**.**2**×**x**=**2x** -
**a**,**b**and**c**are factors of**abc**.

**a**,**b**and**c**are multiplied together to make**abc**.**a**×**b**×**c**=**abc** -
**(x + 1)**and**(x + 2)**are factors of**(x + 1)(x + 2)**.

**(x + 1)**and**(x + 2)**are multiplied together to make**(x + 1)(x + 2)**.**(x + 1)**×**(x + 2)**=**(x + 1)(x + 2)**

## More Factors in Algebra

It would appear that finding factors of a term in algebra is easy. In the example above, we saw that**a**,

**b**and

**c**are factors of

**abc**. It would seem that we would only have to write the letters or numbers or brackets that appear in term to find its factors. While these are all factors, they will not be the only ones. For example,

**1**and the term itself (

**abc**) will also be factors (see

**Note**). Also, any product of these factors are also factors. If

**a**and

**b**are factors,

**ab**is also a factor.

**ac**and

**bc**will also be factors.

# Dividing by Factors

Factors are terms that divide exactly into another term. We have seen that the factors of**abc**are

**a**,

**b**and

**c**. This means that we can divide

**abc**by

**a**,

**b**or

**c**.

**abc**÷

**a**=

**bc**

**abc**÷

**b**=

**ac**

**abc**÷

**c**=

**ab**

**bc**,

**ac**and

**ab**are also factors.

## 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**.

## 1 and the Term Itself Is Always a Factor

1 and the term itself is always a factor of the term. For example,**1**and

**4xy**are both factors of

**4xy**.

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