Factors and Multiples - 1

Factors of a number

A factor of a number is a number that divides the given number with remainder zero.

Example 1

Let the given number = 6

6 ÷ 1 = 6	Quotient = 6	Remainder = 0
6 ÷ 2 = 3	Quotient = 3	Remainder = 0
6 ÷ 3 = 2	Quotient = 2	Remainder = 0
6 ÷ 6 = 1	Quotient = 1	Remainder = 0

Therefore, we can conclude that the numbers 1, 2, 3 and 6 are the factors of the given number 6.

Example 2

Let the given number = 15

15 ÷ 1 = 15	Quotient = 15	Remainder = 0
15 ÷ 3 = 5	Quotient = 5	Remainder = 0
15 ÷ 5 = 3	Quotient = 3	Remainder = 0
15 ÷ 15 = 1	Quotient = 1	Remainder = 0

Therefore, we can conclude that the numbers 1, 3, 5 and 15 are the factors of the given number 15. 

Example 3

Let the given number = 13

13 ÷ 1 = 13	Quotient = 13	Remainder = 0
13 ÷ 13 = 1	Quotient = 1	Remainder = 0

Therefore, we can conclude that the numbers 1 and 13 are the factors of the given number 13.

From the above 3 examples we can observe that for any given number, 1 and the number itself are always the factors.   

In the above examples, numbers 6 and 15 have factors other than 1 and the number itself (6 ad 15 respectively). Whereas the number 13 has only two factors - 1 and 13. 

Activity Time:

• Take 15 matchsticks. 
• Now group them such that each group has 3 matchsticks respectively. How many such groups are formed? Are there any matchsticks remaining?
• Using same number of matchsticks, try to group them such that each group has 5 matchsticks respectively. In this case as well note down how many groups are formed. Also, are there any matchsticks remaining?

Do let me know your answers in the comments section. 

Practice Time:

Find all the factors of following numbers:

a. 11

b. 21 
c. 25
d. 36

Do you know that numbers having only 2 factors have a specific name? Also numbers having more than 2 factors have a specific name, can you name it?

Think over it. We will discuss it in detail, in the next part.