MATHEMATICS

THE STORY OF DIVISIBLE BY 3  

I like watching the registration number of vehicles and play with the numbers...Once walking down the Lane i noticed and came across a startling revelation of divisibility by 3.

The number of car was 7485...now i thought whether this number was divisible by 3….The old method of divisibility by three is add up all the digits and if the sum is divisible then the number too is divisible by three….But that day my mind was preoccupied and it became an arduous task to add up 7+4+8+5...But then 7+4=11 and 8+5=13...i thought if 7+4 were to borrow from 8+5 then, 7+4+1(borrowed from 8+5)=12(divisible by 3). and 8+5-1(1 given to 7+4)=12(divisible by three)....and hence 12+12=24 and 2+4=6, that means 7485 is divisible by 3.

I came to this discovery that however long a number may be...If we pair numbers and then all the pairs are divisible by 3 then the whole huge number will be divisible by 3. in case there are pair of pairs i.e., two pairs that are not divisible by 3, then we can borrow 1 or 2 from these and see if they are divisible…

For eg., consider a number 847758468981...now we pair the nos. 84 77  58 46 89 81

7+7=14

5+8=13

4+6=10

8+9=17

8+1=9(divisible by 3)

But the first four pairs if observed carefully even though not divisible by 3, but if they exchange one with the adjacent pair their sum will be divisible by three and consequently the whole number will be...which in fact if we verify 7+7+5+8+4+6+8+9+8+1=63.

It may not seem significant but adding up two nos instead of all the digits is quicker and also is playful when we borrow and lend 1s and 2s in the balancing act to make it TRIDIVISIBLE.

In case there are odd digits in a huge number we can always append a 0.