Ten divisors

This puzzle is a little harder, but I have included it here for two reasons. One, the python solution can be simple and rely on computer speed to just search all possibilities but a human solution needs to be clever and to cut down the nubmer of possibilites to check. The second reason is that this puzzle was invended by John Conway. John Conway was not only an amazing mathematician but, from all reports, a very decent guy. He died due to coronavirus earlier this year. I encourage you to google him to see some of the things he has done, to start you off have a look at the some of the following

• John Conway’s Game of Life with kids
• A Life in Games: The Playful Genius of John Conway
• John Horton Conway: "On His LOVE/HATE Relationship with LIFE" | Talks at Google
• Look-and-Say Numbers (feat John Conway) - Numberphile

I have a ten digit number, abcdefghij. Each of the digits is different, and

a is divisible by 1
ab is divisible by 2
abc is divisible by 3
abcd is divisible by 4
abcde is divisible by 5
abcdef is divisible by 6
abcdefg is divisible by 7
abcdefgh is divisible by 8
abcdefghi is divisible by 9
abcdefghij is divisible by 10

What’s my number?