140. Find the greatest common divisor of all nine-digit numbers composed of the digits $1,2,3,4,5,6,7,8,9$ (without repetition).
Solution. Each of the 9! such numbers is divisible by 9, since the sum of the digits of each number, which is 45, is divisible by 9. We will prove that 9 is the greatest common divisor of these numbers.

Let the greatest common divisor of the considered numbers be greater than 9. Denote it by $d$. Then the difference between any two of the considered numbers should be divisible by $d$. However, the difference between the numbers 123456798 and 123456789, which is 9, is not divisible by $d$. Therefore, 9 is the greatest common divisor of these numbers.