Hard Series

What is the next number in this series?

4,12,84,3612....




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I have thought of a number that is made up by using all the ten digits just once. Here are a few clues for you to guess my number:

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First two digits are divisible by 2.
First three digits are divisible by 3.
First four digits are divisible by 4.
First five digits are divisible by 5.
First six digits are divisible by 6.
First seven digits are divisible by 7.
First eight digits are divisible by 8.
First nine digits are divisible by 9.
The number is divisible by 10.

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Amazing Facts

Out of the Box

The phrase “thinking outside the box” was popularised from the solution to a topographical puzzle involving 9 dots in a box shape.