Factor – Definition and Examples  

Definition:

A number break up into another numbers that can be multiplied together and get original number.

or

A number that divides into another number exactly and without leaving a remainder is a Factor.

or

A factor is a number that is divisible by another number and the quotient is an integer.

For example: 3 x 6 = 18, therefore, 3 and 6 are the factors of 18.

A number that divides into another number exactly, 

The number 18 is divided by 3 and 6 exactly.

4 x 3 = 12, therefore, 4 and 3 are the factors of 12.

Most numbers have an even number of factors.

Example:    20 ÷ 4 = 5, 

20 exactly divide by 4, and there is no remainder. So we can say that 4 and 5 are the factors of 20.

In the above example, we can break up or simplify the number 20 into its factors, that is 4 and 5. 

In other words, when we multiply 4 and 5, we get 20. 

Now we  break up or simplify the number 4 into its factors, that is 2 and 2.

In other words, when we multiply 2, 2 and 5, we get 20. Therefore, the factors of 20 are 2, 2 and 5. 

Also 2 x 5 = 10, so 10 is also a factor of 20. Again 4 x 5 = 20, so 4 is also factor of 20. 

We can now conclude that the factors of 20 are 1, 2, 4, 5, 10 and 20.

A number can have many factors.

Example:

3 x 2 = 6
 ↙      ↓       ↘
             Factor  Factor   Product

      Factors of 6

Therefore, the factors of 6 are 1, 2, 3, and 6.

Example: 

3 x 4 = 12, so 3 and 4 are factors of 12.

2 x 6 = 12, so 2 and 6 are factors of 12.

1 x 12 = 12, so 1 and 12 are factors of 12.

1, 2, 3, 4, 6, and 12 all are factors of 12.

Example:

Example:

5 x 10 = 50, so 5 and 10 are factors of 50.

2 x 5 = 10, so 2 and 5 are factors of 10.

1 x 50 = 50, so 1 and 50 are factors of 50.

1, 2, 5, 10, and 50 all are factors of 50.

Example:

7 x 7 = 49, so 7 and 7 are factors of 49.

7 x 1 = 7, so 7 and 1 are factors of 7.

1 x 49 = 49, so 1 and 49 are factors of 49.

1, 7, and 49 all are factors of 49.

Facts:

Factors are either composite number or prime numbers.

A prime number has only two factors, the number itself and one.

Number 1 is the smallest factor of every number.

Every number have minimum two factors, 1 and number itself.

Factors are always presented in the form of whole numbers or integers and never in decimals or fractions. 

All even numbers have 2 as their factor.

All numbers that end with 5 will have 5 as their factor.

All numbers ending with 0 and greater than 0 will have 2, 5, and 10 as their factors.