Number Checks

Where a large number of workmen are employed on a building it is customary to provide every man with a little disc bearing his number. 
These are hung on a board by the men as they arrive, and serve as a check on punctuality. 
Now, I once noticed a foreman remove a number of these checks from his board and place them on a split-ring which he carried in his pocket. 
This at once gave me the idea for a good puzzle. In fact, I will confide to my readers that this is just how ideas for puzzles arise. 
You cannot really create an idea: it happens—and you have to be on the alert to seize it when it does so happen.

It will be seen from the illustration that there are ten of these checks on a ring, numbered 1 to 9 and 0. 
The puzzle is to divide them into three groups without taking any off the ring, so that the first group multiplied by the second makes the third group. 

For example, we can divide them into the three groups, 2—8 9 7—1 5 4 6 3, by bringing the 6 and the 3 round to the 4, but unfortunately the first two when multiplied together do not make the third. 

Can you separate them correctly? Of course you may have as many of the checks as you like in any group. 
The puzzle calls for some ingenuity, unless you have the luck to hit on the answer by chance.

See answer

Math Genius