Funny Factorisation

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits $1$ to $9$ each once and only once.


Part 1

The number $4396$ can be written as just such a product. Can you find the factors?


Part 2

Maths is full of surprises! The number $5796$ can be written as a product like this in two DIFFERENT ways, and so can the number $5346$. Can you find these four funny factorisations?

Part 3

Here is another puzzle, again you must use the digits $1$ to $9$ once, but only once, to replace the stars and complete this multiplication example.

This gives six funny factorisations, and there is one more.
You might like to write a computer program to find all seven funny factorisations, or you might come up with a different method.