What are the factors of $711$?
If you have four numbers whose product is $7.11$, you can double one of the numbers and halve one of the others, and the product will still be $7.11$,
you can double one of the numbers, treble another and divide a third by six, and the product will still be $7.11$,
What else can you do that leaves the product unchanged?
This is quite a challenging problem. If you get part of the way and would like more hints, try posting a question on the Please Explain section of the AskNRICH web board.