Digital sum of a number

 

Introduction


Digital sum of a number is the single digit obtained by repeatedly adding the number. It is also called the Digital Root of the number. It is just the sum of all the digits of the number.

For example, Digital Sum of 12 = 1+2 = 3

Digital Sum of 5466 = 5+4+6+6 = 21 = 2+1 = 3

So, the digital sum of 5466 = 3

So, notice that even though sum of the digit of 5466 is 21, 21 is not the digital sum. The sum is again added until we are left with a single digit.

So, can you determine the Digital Sum of :

  • 134566
  • 23566
  • 34563
  • 895785

 

Consider the number 19. The digital sum of 19 is 1+9 = 10 = 1

Consider the number 129. The digital sum of 129 is 1+2+9 = 12 = 3

Consider the number 1239. The digital sum of 1239 is 1+2+3+9 = 15 = 6

So, if a number has 9, this will not have any impact on the digital sum. So, you can safely ignore the digit 9 in the number.

So, can you guess the digital sum of 599992. Ignoring all the 9’s, we are left with 5 and 2. So the digital sum is 5+2=7

Consider another example 7486352. Here, we donot have any 9’s in the number. So, in order to  obtain the digital sum, we will just add all the digits.

Digital Sum of 7486352 = 7+4+8+6+3+5+2 = 35 = 3+5 = 8

 

However, there is a shortcut for this, instead of adding all the digits, cancel out the digits which add up to 9 as shown :

Digital Root1

6 & 3 add upto 9, so we can cancel that. Similarly 5 & 4 adds upto 9 and 7 & 2 adds upto 9. We can cancel all the digits, we are left with the digit 8. So, the digital sum is 8.

So, the question arises,

Why do we need Digital Sum of the number ?


It turns out, when the numbers are added, subtracted, multiplied or divided; their digital sums will also be respectively or added, subtracted, multiplied or divided. So, we can use their digital sums to check the accuracy of the answer.

 

Let’s consider an example :

Digital Root2

Now consider the digital sum of each of the number:

The digital sum of 1234 is 1

The digital sum of 345 is 3

The digital sum of 6543 is 9(or 0)

The digital sum of 345 is 3

So, the total digital sum is 1+3+9+3 = 7

The digital sum of 8467 is 8+4+6+7 is 7

Since the digital sums are equal, we can conclude that the addition is correct.

 

Let’s say you come across a question something like this in the examination :

18265+2736+41328=?

  1. 61329
  2. 62139
  3. 63329
  4. 62329

 

So, instead of adding all the numbers, the shortcut is to obtain the digital sum of each of the numbers.

Let me explain :

The digital sum of 18265 is 4

The digital sum of 2736 is 9( or 0)

The digital sum of 41328 is 9(or 0)

 

So, the total digital sum is 4+9+9 = 4

Let’s look at the choices:

The digital sum of 61329 is 3

The digital sum of 62139 is 3

The digital sum of 63329 is 5

The digital sum of 62329 is 4

So, using Digital sum, we can conclude that only option (4) can be the answer even though we have not actually calculated the sum.

 

Important  It is important to note that, Digital sum sometimes lead to conflicting results.

We know from previous example, the Digital sum of 62329 is 4. So, the digital sum of 62392 is also 4.

In this case, even though the numbers are different, the Digital sum remains the same as the numbers have changed their places.

Digital sum of a number


So, the Moral of the story is, even digital root technique will help you in eliminating few options from the question, it cannot conclusively point out the right answer.

Digital Sum technique can also  be used in case of subtraction, multiplication or division just like we used in addition.

Please contact me if some point in the tutorial is not clear. I would be glad to help.

Kiran Chandrashekhar

Hey, Thanks for dropping by. My name is Kiran Chandrashekhar. I am a full-time software freelancer. I love Maths and Mathematical Shortcuts. Numbers fascinate me. I will be posting articles on Mathematical Shortcuts, Software Tips, Programming Tips in this website. I love teaching students preparing for various competitive examinations. Read my complete story.

7 Comments

  1. kudos to u sir.I was searching for checking perfect square and I came to know this concept too.thx a lot.

  2. Hellloo sir

    Its Brilliant

    I really very like it……

    Thankyou very much for this very useful information 🙂

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