7.2. Find the GCD of all numbers obtained by all possible permutations of the digits of the number 202120222023

Solution. By the divisibility rule, all these numbers are divisible by 9 (the sum of the digits is 18). A sufficient condition to prove that there are no other numbers is that the difference between any two such numbers is also divisible by the GCD. For example, 222222100032 - 222222100023 = 9 is divisible by 9 and cannot be greater than 9.