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
International Standard Book Number the EAN format, and hence could not contain an "X". The 2001 edition of the official manual of the International ISBN Agency says that the <nowiki>ISBN-10</nowiki> check digit – which is the last digit of the ten-digit ISBN – must range from 0 to 10 (the symbol X is used for 10), and must be such that the sum of all the ten digits, each multiplied by its (integer) weight, descending from 10 to 1, is a multiple of 11. For example, for an <nowiki>ISBN-10</nowiki> of 0-306-40615-2: Formally, using modular arithmetic, we can say: It is also true for <nowiki>ISBN-10</nowiki>'s