Persistence of a number assumed. The single-digit final state reached in the process of calculating an integer's additive persistence is its digital root. Put another way, a number's additive persistence counts how many times we must sum its digits to arrive at its digital root. The additive persistence of 2718 is 2: first we find that 2 + 7 + 1 + 8 = 18, and then that 1 + 8 = 9. The multiplicative persistence of 39 is 3, because it takes three steps to reduce 39 to a single digit: 39 → 27 → 14 → 4. Also, 39 is the smallest
Digit sum computer architectures and some programming languages. These operations are used in computing applications including cryptography, coding theory, and computer chess. Harshad numbers are defined in terms of divisibility by their digit sums, and Smith numbers are defined by the equality of their digit sums with the digit sums of their prime factorizations. Digit sum In mathematics, the digit sum of a given integer is the sum of all its digits (e.g. the digit sum of 84001 is calculated as 8+4+0+0+1 = 13). Digit sums are most often computed using the decimal representation of the given number, but they may be