Answer:

Russell found that there are just twelve five-figure numbers that have the peculiarity that the first two figures multiplied by the last three—all the figures being different, and there being no 0—will produce a number with exactly the same five figures, in a different order. 

But only one of these twelve begins with a 1—namely, 14926. 
Now, if we multiply 14 by 926, the result is 12964, which contains the same five figures. 
The number of the motor-car was therefore 14926.

Here are the other eleven numbers:—24651, 42678, 51246, 57834, 75231, 78624, 87435, 72936, 65281, 65983, and 86251.