Alphametic with modulo

Question

Solve this alphametic
??????? mod (? × ? × ? × ? × ? × ? × ?) = 0
example :
????? mod (? × ? × ? × ? × ?) = 0
13248 mod (1 × 3 × 2 × 4 × 8) = 0
Note :

Do not replace any letter with 0.
Each letter represent different digit.
There is only one solution.

Gareth McCaughan · Accepted Answer

A simple computer search quickly yields

Is a computerless solution required?
[EDITED to add the following: first steps toward a computerless answer.]

Lynn · Answer

Alphametic with modulo

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