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
Check digit January 2007) is equal to the EAN-13 code found underneath a book's barcode. Its check digit is generated the same way as the UPC except that the even digits are multiplied by 3 instead of the odd digits. EAN (European Article Number) check digits (administered by GS1) are calculated by summing each of the odd position numbers multiplied by 3 and then by adding the sum of the even position numbers. Numbers are examined going from right to left, so the first odd position is the last digit in the code. The final digit of the result is subtracted from