# multiplicative digital root

Given an integer $m$ consisting of $k$ digits $d_{1},\dots,d_{k}$ in base $b$, let

 $j=\prod_{i=1}^{k}d_{i},$

then repeat this operation on the digits of $j$ until $j. This stores in $j$ the multiplicative digital root of $m$. The number of iterations of the multiplication operation is called the multiplicative persistence of $m$.

Title multiplicative digital root MultiplicativeDigitalRoot 2013-03-22 16:00:42 2013-03-22 16:00:42 CompositeFan (12809) CompositeFan (12809) 4 CompositeFan (12809) Definition msc 11A63 repeated digit product repeated digital product multiplicative persistence