# multiplicative digital root

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

$$j=\prod _{i=1}^{k}{d}_{i},$$ |

then repeat this operation^{} on the digits of $j$ until $$. 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 |
---|---|

Canonical name | MultiplicativeDigitalRoot |

Date of creation | 2013-03-22 16:00:42 |

Last modified on | 2013-03-22 16:00:42 |

Owner | CompositeFan (12809) |

Last modified by | CompositeFan (12809) |

Numerical id | 4 |

Author | CompositeFan (12809) |

Entry type | Definition |

Classification | msc 11A63 |

Synonym | repeated digit product |

Synonym | repeated digital product |

Defines | multiplicative persistence |