# 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.

#### An Example Question

What are the factors of the term shown below?

Step 1

Find the factors of the number. In our example, the number is 2.

The factors of 2 are 1 and 2.

Step 2

Find each letter or bracket that appears in the term.

In our example, x is the only letter.

Step 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.

#### An Example Question

What are the factors of the term shown below?

Step 1

Find the factors of the number. In our example, the number is 4.

The factors of 4 are 1, 2 and 4.

Step 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.

Step 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) 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.

# Another Real Example of How to Find Factors in Algebra

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

Algebra Lessons
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# 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 multipled 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.