Digit Sum

What is a digit?

“Digit” is derived from Latin word digitus meaning ‘finger, toe’. Digit means any numeral below 10, i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

And “Sum” means to add.

A “Digit Sum” is the sum of all of the digits of a number, and is found by adding all of the digits of a number.

For example:

  1. The Digit Sum of 32 is 3+2 = 5
  2. The Digit Sum of 152 is 1+5+2 = 8

If the sum of the digits is greater than 9, then sum the digits of the result again until the result is less than 10.

For example:

  1. The Digit Sum of 57 is 5+7 = 12 → 1+2 = 3 ….. Here 12 >9, so sum the digits again.
    So the Digit Sum of 57 is 3.
  2. The Digit Sum of 687 is 6+8+7 = 21 → 2+1 = 3…. Here 21 >9, so sum the digits again.
    So the Digit Sum of 687 is 3.

Keep finding the Digit Sum of the result until it’s less than 10. Also, in case of digit sum, 0 and 9 are equivalent!

Why is digit sum important?

Digit sum is used for checking calculations, and this becomes highly useful where large numbers are involved. I will explain this part in subsequent sections.

In this course, we are going to study about below topics:

  • Nine Point Circle
  • Casting Out nines (9s)
  • Checking with Digit Sums
  • A magic number


Quick calculations can be performed more easily if the numbers are split into more “manageable parts”. The best part of Splitting is that it helps us do the calculations mentally and can be applied to Addition, Subtraction, Multiplication and Division.

What is important in Splitting is to find the correct place to split so as to avoid carry.

Splitting can be used for any operation, viz. Addition, Subtraction, Multiplication, and Division.

I will explain you all with the help of examples for each of above cases.

Divisibility Check

Division is opposite of multiplication, and is repeated subtraction.

There is a unique pattern in division, that will help you to find whether any number is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12 or so on.

In this topic, we are going to learn how to check if a number is divisible by any of the above numbers without actually dividing it.

Let us compare the Traditional way of divisibility check with Vedic way.

Is 24567890 is divisible 3?

Traditional way:

The traditional way is very lengthy and takes time to check divisibility.

division traditional.PNG

Vedic Way:

Check if sum of all digits of this number is divisible by 3.

Sum of digits = 2+4+5+6+7+8+9+0 = 41

Since 41 is not divisible by 3, so number 24567890  is also not divisible by 3.

In this topic, we are going to cover divisibility check by numbers 2, 3, 4, 5, 6, 7, 8, 9, and 10.