TESTS OF DIVISIBILITY

(J). Divisibility by 6 :

A number is divisible by 6 only when it is divisible by 2 and 3 both. So first of all we see that the number is even or not then we check for the divisibility by 3 .

Example ; (1) check whether 216 is divisible by 6 or not .
Solution : step (a). First of all we check the given number is divisible by 2 or not
Since unit digit is divisible by 2 then the given number is divisible by 2 .

Step (2). We see that the given number is divisible by 2 so now we check whether the given number is divisible by 3 or not .
Sum of digits of the given number is (6+1+2) 9 , which is divisible by 3 so the given number is divisible by 3 also .

Step(3). Since the given number is divisible by 2 and 3 both so the given number is divisible by 6 also .

(K). Divisibility by 12 :

 A number is divisible by 12 only when it is divisible by 4 and 3 both at the same time . so first of all check the divisibility by 4 then by 4 .

NOTE : Thus we can conclude that any number which is divisible by a composite number( The natural numbers which are not prime , are called composite numbers) ,as mentioned above , must be divisible by all its factors whose L.C.M is the given number divisior .