first, get the factorization of 693:

693 = (3^2)(7)(11)

now, start finding such that it has factors7and11whosepowersareodd, and other integer factors whose powers areeven.

for example: N= (7)(11)(2^2) = 308 and you are correct..

N= (7)(11)(3^2) = 693

N= (7)(11)(4^2) = ?.. just make sure that is still a 3 digit number..

EDIT: basically, i chose 1 as the powers of 7 and 11, since it it were 3 or higher odd powers, then it will give you not a three digit number.. EX: (7^3)(11) = 3773