The Lesson

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.

Real Examples of Factors in Algebra

It is easier to understand factors with examples.
  • 2 and x are factors of 2x.

    2 x 2 and x are multiplied together to make 2x.
    2 × x = 2x
  • a, b and c are factors of abc.

    a b c a, b and c are multiplied together to make abc.
    a × b × c = abc
  • (x + 1) and (x + 2) are factors of (x + 1)(x + 2).

    bracket x + 1 bracket x + 2 (x + 1) and (x + 2) are multiplied together to make (x + 1)(x + 2).
    (x + 1) × (x + 2) = (x + 1)(x + 2)

More Factors in Algebra

It would appear that finding factors of a term in algebra is easy. In the example above, we saw that a, b and c are factors of abc. It would seem that we would only have to write the letters or numbers or brackets that appear in term to find its factors. While these are all factors, they will not be the only ones. For example, 1 and the term itself (abc) will also be factors (see Note). Also, any product of these factors are also factors. If a and b are factors, ab is also a factor. ac and bc will also be factors.

Dividing by Factors

Factors are terms that divide exactly into another term. We have seen that the factors of abc are a, b and c. This means that we can divide abc by a, b or c.

abc ÷ a = bc

abc ÷ b = ac

abc ÷ c = ab

Notice that the term you get when you divide by one factor gives another factor: bc, ac and ab are also factors.

Lesson Slides

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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.

1 and the Term Itself Is Always a Factor

1 and the term itself is always a factor of the term. For example, 1 and 4xy are both factors of 4xy.