Factor Definition

If a number leaves a reminder “0” while dividing another number, then it is called to be the Factor of that divisible number.

For example

If you are dividing 12 by 4, then 4 will be a factor of 12 because it leaves a remainder in the end.

We can also define Factor in another way

The numbers that we multiply to get the resultant will be called the factors of the resultant number.

For example

We get 12 by multiplying 3 and 4. It means that 3 and 4 are the factors of the 12.

Are factors and multiples the same?

No, Factors and multiples are referred to two different numbers or conditions. Multiples are those numbers that come in the way while we are pronouncing a table of any number.

For example

3, 6, 9, and 12 are multiples of “3” because these numbers can be divided by 3.


You can read about “Multiples” in detail here on this page of our tool.

Representation of Factors

There is no specific representation of Factors in general Mathematics. But it can be shown distinctly in Algebra.

For instance, you may get factors like (x + 3) (x - 7), etc in algebra. These are called factors because both of these are multiplied by each other to get the result.

Fun Facts about Factors

  • Two negative factors always give a positive result
  • Two factors with opposite signs always give a negative number in the result.
  • A number can't have a single factor but it always has at least two factors.


Is factor have any other name?

In Mathematics, Factors are also called roots of the same number. In simple words, you can say that 3 is the root of 12 instead of saying 3 is the factor of the root.

What is the importance of factors?

Finding factors has great importance because it helps the students learn different techniques. You must have to learn how to find "Prime Factors" to solve a question for finding LCM and HCF.

How can we find a factor of a particular number?

To find factors of any particular number, you have to divide that number with your set of words. The numbers that will leave a reminder at the end will be called the factors of that number.