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
Elementary arithmetic tens-digit of the sum of a pair of digits is called the "carry digit". For simplicity, consider only numbers with three digits or fewer. To add a pair of numbers (written in Arabic numerals), write the second number under the first one, so that digits line up in columns: the rightmost column will contain the ones-digit of the second number under the ones-digit of the first number. This rightmost column is the ones-column. The column immediately to its left is the tens-column. The tens-column will have the tens-digit of the second number (if it has one) under the tens-digit of