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Consider the integer 384. Multiplying its digits, $$3 \times 8 \times 4 = 96$$ and $${{384} \over {96}} = 91.$$
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 $d_x$ (for $x \le k$ is an integer of $n$
$${\prod_{i = 1}^m d_i}|n$$
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 $1 \times 7 \times 2 \times 8 = 112$ . The reverse is also possible (for example, 384 is divisible by 96, as shown above, but clearly not by its multiplicative digital root 0).
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- J. J. Tattersall, Elementary number theory in nine chapters, p. 86. Cambridge: Cambridge University Press (2005)
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