How to Find Factors in Algebra
Finding Factors in Algebra
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?
StepbyStep:
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.
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?
StepbyStep:
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^{2} are factors.

The only bracket is (y + 1).
(y + 1) is a factor.
3
The term itself is also a factor. In our example, 4x^{2}(y + 1) is the term.
Answer:
The factors of 4x^{2}(y + 1) are:
Products of Factors Are Also (Usually) Factors
While 1, 2, 4, x, x^{2}, y + 1 and 4x^{2}(y + 1) are all factors of 4x^{2}(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) cannot be a factor.

x and x^{2} are both factors, but their product x^{3} can not be a factor.
Any product of letters cannot have an exponent greater than the exponent of the letter in the term (x^{2} in our example).

4x^{2}(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.