Question on Finding unknown Number in the Sequence

Topic : Finding Unknown Number

Question : There is a certain 6-digit number that, when multiplied by 6, the first 3 digits switch places with the second 3 digits. (For example, 123456 becomes 456123). What is this number?

Solution :
Let the number be abcdef. 6(abcdef)= defabc.
Let the value of abc=X and def=Y .
6(1000x+y) = 1000y+x.
5999x=994y.
Y=5999/994x
=(857/142)x.
Since x,y are three digit integers x=142 and y=857.
So the number is 142857