The solution to this problem requires the knowledge of an essential fact or observation that the cube of any integer is congruent to 0, 1 or 6 mod 7.
Solution:
The first thing to note in this kind of problem is the prime factorization of the given factor of n, in this case, 55 = 5 * 11. In most of such problems, the given factor will have easy prime factors whose divisibility tests you are…