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.

* | * | $9$ | |

$\times$ | $4$ | * | |

--- | --- | --- | --- |

* | $6$ | * | * |

*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. *