Sum of the Digits

J

Jitzy

J K
Heeey Guys,,,,
Do you want to Demistify the sum of Digits of A number concept..

In the decimal system we have only 10 digits.
So if the some of the digits of a number becomes 9 We have to part with the singleton approach and Use 2 digits to represent the SUM.

tHIS can be considered as the Modulo 9.
Whenver you u are calculating the Sum of a number Just skip that 9 in it.

Now Suppose you have a number with some of digits as 9,
You can muntiply this number with any number in this world.
The sum would always remain 9 .Because of you desirous of finding 9 times of Something..:SugarwareZ-064:
 
Jitzy said:
Heeey Guys,,,,
Do you want to Demistify the sum of Digits of A number concept..

In the decimal system we have only 10 digits.
So if the some of the digits of a number becomes 9 We have to part with the singleton approach and Use 2 digits to represent the SUM.

tHIS can be considered as the Modulo 9.
Whenver you u are calculating the Sum of a number Just skip that 9 in it.

Now Suppose you have a number with some of digits as 9,
You can muntiply this number with any number in this world.
The sum would always remain 9 .Because of you desirous of finding 9 times of Something..:SugarwareZ-064:
Click to expand...
Hi,
Thanks the process seems to be good, but i'll appreciate if u can illustrate the same with an example. Then it will become clear.
 
Consider it done gaurav..
Let us muntiply 2 & 8 =16
so the sum of the digits would be 7.

Now we mutiply it it 12, so 12*8=96. Sum of digits is 6.

You can see that SOD of 12 =3 and that of 8 is 8 . Now if you muntiply the SODs of the two numbers you would get 24 where the final SOD is again 6.

Same in the first case. SOD of 02 is 2 And that of 08 is 8. The product of these SODs is 16,And its SOD is 7.

So finally here is the trick. Sum of digit of a number is equal to that of the Muntiplicants of the Number.

Now let us dive into the modulo 9 funda.
We have 9 .Muntiply 9 by any number 2,3,4,5 you would see that you get the results as 27,36,45,54,63,72,81 etc
The SOD of all of them is 9.

same for any number which is divisible by 9, or in other words has SOD as 9.
Let us check for 11111111111.
the sod is 9 ,
If we muntiply it with 2 we get 222222222.
The sod here is 18=9
If we muntiply 111111111 with 3 the SOD here is 36=9.
So we see that if we can find a single factor of a number as 9.
The Sod always remains as 9.
 
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