Tuesday, January 02, 2007

Casting Out Nines

How do you check the answer of a large multiplication like 8216*4215=36430440 without actually doing the multiplication.

Sum 8+2+1+6=17. Take modulo 9 = 8.
Sum 4+2+1+5=12. Take modulo 9 = 3.

Sum 3+6+4+3+4+4=24. Take modulo 9 = 6.

Now check 8*3=24 and 2+4 = 6.
at

2 comments:

  1. Anonymous2/12/2007 6:27 AM

    This means that if u have a no like
    36421440...
    According to ur calculation it will come out as the rt result...?

    ReplyDelete
  2. Mayank4/21/2007 4:06 AM

    certainly not :) !! i guess this is a necessary condition not a sufficient one. we can use this for a fast random check only to see if this is not satisfied

    ReplyDelete