# Finding Factors in Algebra(KS3, Year 7)

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The factors of a term can be found.

## 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?

## 1

Find the factors of the number. In our example, the number is 2. The factors of 2 are 1 and 2.

## 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.

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?

## 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 x2 are factors.
• The only bracket is (y + 1). (y + 1) is a factor.

## 3

The term itself is also a factor. In our example, 4x2(y + 1) is the term.

The factors of 4x2(y + 1) are:

## Products of Factors Are Also (Usually) Factors

While 1, 2, 4, x, x2, y + 1 and 4x2(y + 1) are all factors of 4x2(y + 1), they are not the only factors. Other factors can be found by multiplying these factors together. For example,
• 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.
Be careful, not all the products of these factors are factors For example,
• 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 x2 are both factors, but their product x3 can not be a factor. Any product of letters can not have an exponent greater than the exponent of the letter in the term (x2 in our example).
• 4x2(y + 1) 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.

## Lesson Slides

The slider below shows another real example of finding the factors of a term in algebra.

## 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.

This page was written by Stephen Clarke.

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