Factors and Multiples

Factors

Let’s start with division of 6. We can divide the given number by a number less than or equal to the given number.

So, number 6 can be written as:

6 = 1 × 6;

6 = 2 × 3;

6 = 3 × 2;

6 = 6 × 1;

Therefore numbers 1, 2, 3 and 6 are exact divisors of 6.

These numbers are called factors of 6.

So, factors are what we can multiply to get the number.

Or we can say, numbers that divides a given number completely i.e., without leaving remainder is called a factor of the given number. A factor is also called a divisor. A number can have many factors.

Multiples

Example:

6 = 2 x 3

8 = 2 x 4

From the above example we conclude that a multiple is the product of a number and an integer.

Let’s find out the multiple of 2.

2 x 1 = 2

2 x 2 = 4

2 x 3 = 6

2 x 4 = 8 and so on

Therefore, multiple of 2 are obtained by multiplying it by a natural number.

Facts about Factors and Multiples

1. 1 is a factor of every number. Example: 5 = 1 × 5, 9 = 1 × 9 and so on

2. Every number is a factor of itself. Example: We can write 12 as 12 = 12 × 1.

3. Every factor of a number is an exact divisor of given number. Example: Factors of 8 are 1, 2, 4 and 8. So, 1, 2, 4 and 8 are exact divisor of 8.

4. Every factor is less than or equal to the given number. Example: Factor of 34 are 1, 2, 17 1nd 34 itself.

5. Number of factors of a given number is finite. We can count the number of factors of even larger numbers.  

6. Every multiple of a number is greater than or equal to the given number. Example: Multiple of 3 are 3, 6, 9, 12, 15…

7. Number of multiples of a given number is infinite. Example: Multiple of 2 are 2, 4, 6, 8, 12, 15 …… The list is endless.

8. Every number is a multiple of itself. Example:  6 = 6×1.

9. A number for which sum of all its factors is equal to twice the number is called a perfect number.

Example: Factors of 6 are 1, 2, 3 and 6.

Sum of all its factors = 1+2+3+6 = 12

12 = 2 × 6 (sum = 2 of the number)