# What is this Number?

N is a number where each digit is divisible by its place, for example:

1527

1 has to be divisible by 1, 5 divisible by 2, 2 divisible by 3, and 7 divisible by 4.

Additionally, N must be divisible by all of its digits.

It has to be at least 5 digits long, and have at least 3 different digits.

Does N exist? Is there more than 1 number that fits N? If so is there a pattern? Give a few examples.

• The identity that $n$ divides $n$ makes this very, very easy. – Aza Nov 2 '14 at 1:37
• @Emrakul Exactly what do you mean by that... – warspyking Nov 2 '14 at 9:45