Help a man to recover his PIN number?

Question

A man forget his 6 digits PIN number, but fortunately he remembers the clue for his PIN number.

The n-th digit is the first digit of (product of other digits multiplied by n)
The number is not 000000

If the pin is abcdef, then :

The 1st digit = The first digit of 1×b×c×d×e×f
The 2nd digit = the first digit of 2×a×c×d×e×f
...
The 6th digit = The first digit of 6×a×b×c×d×e

What is his pin number ?

Answer 1

Finally I had to brute force the answer using a c code as I couldn't figure out the analytical approach to this answer.
It is 529311.
The code is below:

Answer 2

111111 shall be answer.

Comments

There won't be a second digit for the product in the next step.

---

ie., product is 2 in the next step making 2=b then it will be 3=c and so on which contradicts your initial assumption. Hence further iteration needed.

Answer 3

777777 is one solution.
Just do 1x2x3x4x5x6=720 to match all possibilities

Comments

1*7*7*7*7*7 = 16807 and it's first digit is 1 contradicting initial assumption of 7.