Mystery Number 5
There is a ten-digit mystery number (no 0 at the beginning), represented by ABCDEFGHIJ, where each numeral, from 0 to 9, is used only once. Being given the following clues, what is the number?
1) A + B + C + D + E is divisible by 6.
2) F + G + H + I + J is divisible by 5.
3) A + C + E + G + I is divisible by 9.
4) B + D + F + H + J is divisible by 2.
5) AB is a divisible by 3.
6) CD is a divisible by 4.
7) EF is a divisible by 7.
8) GH is a divisible by 8.
9) IJ is a divisible by 10.
10) FE, HC, and JA are all prime numbers.