TIMO - 2018 - Grade 8 - Heat Round - Paper 4 Question 1

Find the 3-digit number $\overline{ACA}$. The non-zero digits $A,C$ satisfy: (1) $\overline{CAC}$ is divisible by 9; (2) $\overline{CCA}$ is divisible by 7; (3) $\overline{ACC}$ has an odd number of factors.