Introduction to Factors and Multiples ?

What are Factors and Multiples ?

Factors

• The numbers which exactly divides the given number are called the Factors of that number.
• Example :
  

Factors of the number 12  are

1 × 12,

2 × 6,

3 × 4,

4 × 3,

6 × 2 and

12 ×1

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

Multiples

If we say that 4 and 5 are the factors of 20 then 20 is the multiple of 4 and 5 both.

List the multiples of 3

3 × 1 = 3

3 × 2 = 6

3 × 3 = 9

3 × 4 = 12

and so on ,

Hence multiples of 3 are 3,6,9,12,15,18........

• Multiples are always more than or equal to the given number.

Some facts about Factors and Multiples

•     1 is the only number which is the factor of every number.
•     Every number is the factor of itself.
•     All the factors of any number are the exact divisor of that number.
•     All the factors are less than or equal to the given number.
•     There are limited numbers of factors of any given number.
•     All the multiples of any number are greater than or equal to the given number.
•     There are unlimited multiples of any given numbers.
•     Every number is a multiple of itself.

Perfect Number

• If the sum of all the factors of any number is equal to the double of that number then that number is called a Perfect Number.

• Perfect Number	Factors	Sum of all the factors
  6	1, 2, 3, 6	12
  28	1, 2, 4, 7, 14, 28	56
  496	1, 2, 4, 8, 16, 31, 62, 124, 248, 496

Common Factors and Common Multiples

Example: 1

What are the common factors of 25 and 55?

Solution:

Factors of 25 are 1, 5.

Factors of 55 are 1, 5, 11.

so Common factors of 25 and 55 are 1 and 5.

Example: 2

Find the common multiples of 3 and 4.

Solution:

Common multiples of 3 and 4 are 0, 12, 24 and so on.