DIGITAL ROOTS

Digital root is a concept we all know but hardly use. All of us have used digital roots to check the divisibility of 3 and 9 but its application are lot more than this. It can be used to check the correctness of addition, subtraction, multiplication, division and lots more.

CONCEPT 1

What is digital roots ?

Digital root is sum of all the digits of a number, continued until there is only one digit left.

Eg. 1. Digtal root of 123 is 1+2+3=6

Eg. 2. Digital root of 563281 is 5+6+3+2+8+1=25 again 2+5=7,

so digital root of 563281 is 7.

I hope its clear,please post your doubts.

CONCEPT 2

CASTING OUT NINE METHOD

(Elimination and Retention)

Lets try to find out the digital root of 2637896.So 2+6+3+7+8+9+6 = 41 then again 4+1=5 so digital root is 5.

So we have observed that finding the digital root of large numbers is actually a cumbersome process. That's why this method gives a faster way for calculating digital roots.

In casting out nine method, we eliminate 9 or group of digit add upto 9. Then the numbers which are left at the end are added up for the digital root. Lets understand this by some examples:-

Eg 1. Digital Root of 93 is 3 ( as we have cast out nine and the number 3 is the digital root.)

Eg.2 Digital root of 732 is 3 ( as we have cast out 7+2makes 9 hence 3 is the digital root.)

Eg.3 Digital root of 9743821 is 7 ( as we cast out 9, 7&2 and 8&1 so 4 &3 are added to get 7 so 7 is the digital root.)

Just try to gain expertise, by practise.