Editing Persistence of a number (section)

{{Short description|Property of a number}}
In [[mathematics]], the '''persistence of a number''' is the number of times one must apply a given operation to an [[integer]] before reaching a [[Fixed point (mathematics)|fixed point]] at which the operation no longer alters the number.

Usually, this involves additive or multiplicative persistence of a non-negative integer, which is how often one has to replace the number by the sum or product of its digits until one reaches a single digit. Because the numbers are broken down into their digits, the additive or multiplicative persistence depends on the [[radix]]. In the remainder of this article, [[base ten]] is 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 [[digit sum|sum its digits]] to arrive at its digital root.