DIGITAL ROOT OF A NUMBER

The word 'digit' means the single figure number. The following ten single figure numbers are called digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Digital Sum :

In math, the term 'digital sum' means the sum of all digits in the given number.

For example, consider the number 978654.

Sum of all digits in 978654 :

= 9 + 7 + 8 + 6 + 5 + 4

= 39

So, the digital sum of 978654 is 39.

Digital Root :

Finding digital root of a number is the similar process to find digital sum.

To find digital root of a number, add all the digits in the number.

Case (i) :

If the sum of all the digits in the number is a single digit value, then it's the digital root of the number.

For example, consider the number 43.

Sum of the digits in 43 :

= 4 + 3

= 7

Sum of the digits in 43 is a single digit value, that is 7.

Therefore, the digital root of 43 is '7'.

Case (ii) :

If the sum of all the digits in the number is a value more than 9, add the digits of the sum. The single digit obtained at the end is the digital root of the number.

For example, consider the number 75.

Sum of the digits in 75 :

= 7 + 5

= 12

Here, the sum of the digits in 75 is '12' which is more than 9.

So, add the digits in the sum 12.

= 1 + 2

= 3

Therefore, the digital root of 75 is '3'.

Note :

The digital root of any natural number will always be a single digit value.

Shortcut to Find Digital Root

Casting Out 9's

Digital root of 29 :

= 2 + 9

= 11

11 ----> 1 + 1 = 2

Digital root of 529 :

= 5 + 2 + 9

= 16

16 ----> 1 + 6 = 7

Digital root of 1239 :

= 1 + 2 + 3 + 9

= 15

15 ----> 1 + 5 = 6

From the above calculations, if a number has the digit 9, it will not have any impact in the digital root.

So, you can ignore the digit 9 or the digits add up to 9 in the number when you find digital root.

Note :

1. If all the digits in a number are 9, then the digital root of the number is also '9'.

2. In a two digit number, if the two digits add up to 9 and nothing is left over, then the digital root is also '9'.

3. In a five digit number, if two digits add up to 9 and the remaining three digits also add up to 9 and nothing is left over, then the digital root of the number is '9'.

4. In a six digit number, if two digits add up to 9 and the remaining three digits also add up to 9 and you are left with the digit '0', then the digital root of the number is '9'.

4. In a six digit number, if two digits add up to 9 and the remaining three digits also add up to 9 and you are left with the digit 'k' (≠ 0), then the digital root of the number is 'k'.

Example 1 :

Find the digital sum of 36.

Solution :

To find the digital sum, add the digits in 36.

= 3 + 6

= 9

The digital sum of 36 is '9'.

Example 2 :

Find the digital sum of 320.

Solution :

To find the digital sum, add the digits in 320.

= 3 + 2 + 0

= 5

The digital sum of 320 is '5'.

Example 3 :

Find the digital sum of 1256.

Solution :

To find the digital sum, add the digits in 1256.

= 1 + 2 + 5 + 6

= 14

The digital sum of 1256 is '14'.

Example 4 :

Find the digital sum of 20356.

Solution :

To find the digital sum, add the digits in 20356.

= 2 + 0 + 3 + 5 + 6

= 16

The digital sum of 20356 is '16'.

Example 5 :

Find the digital root of 36.

Solution :

To find the digital root, add the digits in 36.

= 3 + 6

= 9

Sum of the digits in 36 is a single digit value 9.

So, the digital root of 36 is '9'.

Example 6 :

Find the digital root of 10.

Solution :

To find the digital root, add the digits in 10.

= 1 + 0

= 1

Sum of the digits in 10 is a single digit value 1.

So, the digital root of 10 is '1'.

Example 7 :

Find the digital root of 438.

Solution :

To find the digital root, add the digits in 438.

= 4 + 3 + 8

= 15

Here, the sum of the digits in 438 is '15' which is more than 9.

So, add the digits in the sum 15.

= 1 + 5

= 6

Therefore, the digital root of 438 is '6'.

Example 8 :

Find the digital root of 7999992.

Solution :

Ignoring all 9's in 7999992, we are left with 7 and 2.

= 7 + 2

= 9

Therefore, the digital root of 7999992 is '9'.

Example 9 :

Find the digital root of 7826345.

Solution :

Find the digits in 7826345 which add up to 9.

7826345

Ignoring the digits which add up to 9, we are left with 8.

'8' is a single digit value.

Therefore, the digital root of 7826345 is '8'.

Example 10 :

Find the digital root of 907236.

Solution :

Find the digits in 907236 which add up to 9.

907236

Ignoring the digit 9 and the digits which add up to 9, we are left with the digit zero.

Therefore, the digital root of 907236 is '9'.

Example 11 :

Find the digital root of 72554.

Solution :

Find the digits in 72554 which add up to 9.

72554

Ignoring the digits which add up to 9, we are left with the digit 5 (≠ 0).

Therefore, the digital root of 72554 is '5'.

Example 12 :

Find the digital root of 613481.

Solution :

Find the digits in 613481 which add up to 9.

613481

Ignoring the digits which add up to 9, we are left with the digits 1 and 4.

= 1 + 4

= 5

Therefore, the digital root of 613481 is '5'.

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DIGITAL ROOT OF A NUMBER

Shortcut to Find Digital Root

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