Zuckerman number

Consider the integer 384. Multiplying its digits,




When an integer is divisible by the product of its digits, it’s called a Zuckerman number. That is, given m is the number of digits of n and dx (for xk) is an integer of n,


All 1-digit numbers and the base number itself are Zuckerman numbers.

It is possible for an integer to be divisible by its multiplicative digital root and yet not be a Zuckerman number because it doesn’t divide its first digit product evenly (for example, 1728 in base 10 has multiplicative digital root 2 but is not divisible by 1×7×2×8=112). The reverse is also possible (for example, 384 is divisible by 96, as shown above, but clearly not by its multiplicative digital root 0).


Title Zuckerman number
Canonical name ZuckermanNumber
Date of creation 2013-03-22 16:04:36
Last modified on 2013-03-22 16:04:36
Owner CompositeFan (12809)
Last modified by CompositeFan (12809)
Numerical id 4
Author CompositeFan (12809)
Entry type Definition
Classification msc 11A63