Step 6: Vedic Multiplication Example: 3-Digit by 3-Digit
Example 3: 341*562
At this point, some of the faint of heart may be reaching for their calculators. Be strong, you can handle this using the vedic technique with relative ease (and considerably less writing) than that which you probably learned in elementary school.
1) Ones Digit: 2*1 = 2
2) Tens Digit: 2*4+6*1 = 8+6 = 14 (write a 4, carry a 1)
3) Hundreds Digit: 2*3+4*6+5*1 = 6+24+5 = 35 (write a 5, carry a 3)
Notice at this point that we have reached the end of the top number, that is to say, 2 can not be multiplied by anything else, as there are no more digits. Thus, for the thousands digit we shall multiply 6 and 3 first, and then for the ten thousands digit, 5 and 3. (read on for the steps)
4) Thousands Digit: 6*3 + 5*4 = 18+20 = 38 (write an 8, carry a 3)
5) Ten Thousands Digit: 5*3 = 15 (we've reached the end of the multiplication, so feel free to simply write 15 rather than carry a 1)
6) Add in the carries to produce the final answer: 191642 (verified via calculator)
At this point it should be noted that the 2 numbers need not have the same number of digits. For example, if a 3-digit number were to be multiplied by a 2-digit number, just follow the formula for 3-digit by 3-digit multiplication and just pad out the missing digits with zeros.