Divisibility rules - 3, 6 and 9

 Quote : If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.      

 -- Tobias Dantzig

How can you find a number is divisible by 3 or 6 or 9 ?

Very simple. Just find the sum of all digits in the number.

if sum is divisible by 3, the number is divisible by 3

if sum is divisible by 9, the number is divisible by 9

if sum is divisible by 3 and unit place digit is 0 or 2 or 4 or 6 or 8, the number is divisible by 6.

Lets look at examples.

a) 156
     step1 : sum = 1 + 5 + 6 = 12
     step2 : 12 is divisible by 3. So 156 is divisible by 3

b) 2345678
    sum = 2 + 3 + 4 + 5 + 6 + 7 + 8 = 35
    35 is not divisible by 3. So 2345678 is not divisible by 3
c) Is 135678 divisible by 9?
    sum = 1 + 3 + 5 + 6 + 7 + 8 = 30
    30 is not divisible by 9. So 135678 is not divisible by 9
d) Is 127 divisible by 6 ?
    unit place digit is 7. So 127 is not divisible by 6 ( Unit place digit should be 0 or 2 or 4 or 6 or 8 )

e) Is 1296 divisible 3 or 6 or 9 ?
    sum = 1 + 2 + 9 + 6 = 18

    18 is divisible by 3. So 1296 is divisible by 3

    18 is divisible by 9. So 1296 is divisible by 9

    Unit place digit is 6 and 18 is divisible by 3. So 1296 is divisible 6.

Check following numbers are divisible by 3 or 6 or 9
145678, 23567, 98741