The digital root of a number is obtained by summing its digits and then repeating the process (summing the sum's digits) until the answer is a single digit number. For example, the digital root of 7368 is 6.

Determine the digital root of (9⁷²⁴⁰+38)⁸⁴⁵⁷

Having a natural number A and adding to it 9 has the effect of adding nothing to it's digital root because for example, 5+9
= 4 + 1 + 9 = 10 + 4  as you see the 9 is "absorbed" with one unit and a unit is added to the next factor of power of 10,so -1+9+1-9 = 0, as we clearly see now the digital root of 5 is equal to the digital root of 14,23,32,41 etc. and general the digital root of A E {[0,9]} + 9n, n E N = A, the digital root can be computed by:

DR(A) = ((A-1) MOD 9)+1

Posted by John on 2006-07-10 05:02:29