How to Find Factors in Algebra

Finding Factors in Algebra

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) cannot be a factor.

  • x and x2 are both factors, but their product x3 can not be a factor.

    Any product of letters cannot 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.

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See Also

What is algebra? What is a term in algebra? What is a factor? What is an exponent?