Digital Root

Digital Root

The digital root or remainder of a whole number is the iterative sum of the values associated with each of its digits.

Casting out nines uses the digital root of a number.


  • Consider the number 457.
    We add the values associated with each of its digits, then repeat the process with the values associated with the digits of the number obtained, and so on, until there is only one digit left.
    4 + 5 + 7 = 16 and 1 + 6 = 7.
    The digital root of 457 is 7.
  • Consider the number 4589.
    4 + 5 + 8 + 9 = 26 and 2 + 6 = 8.
    The digital root of 4589 is 8.

Educational Note

The concept of the digital root of a number is unfortunately not used very much in teaching. It can be very useful to verify some characteristics of divisibility. The digital sum is also useful for this.

It can also be used to show certain properties of certain numbers, such as:

The digital root or the remainder of a number can also be studied using congruence modulo n.

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