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Finding Factors in Algebra
(KS3, Year 7)
The Lesson
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?StepbyStep:
1
2
Find each letter or bracket that appears in the term.
In our example, x is the only letter.
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.
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.
 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^{2} are both factors, but their product x^{3} 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^{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.
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. Do you disagree with something on this page?
 Did you spot a typo?