Finding Factors in Algebra
(KS3, Year 7)
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?
2 x

Step-by-Step:

1

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

2

Find each letter or bracket that appears in the term. 2 x 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: 1, 2, x, 2x

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?
4 x squared times y plus 1

Step-by-Step:

1

Find the factors of the number. In our example, the number is 4. 4 x squared times y plus 1 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). term with x squared highlighted 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). term with y plus 1 highlighted (y + 1) is a factor.

3

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

Answer:

The factors of 4x2(y + 1) are: 1, 2, 4, x, x squared, y + 1

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.
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This page was written by Stephen Clarke.