number theory - Find the least non negative residues mod 7,11 and 13 of 12345678.

Find the least non negative residues mod 7,11 and 13 of 12345678.

my attempt: A number N is congruent modulo 7, 11, or 13, to the alternating sum of its digits in base 1000. (For example, 123456789 ≡ 789 − 456 + 123 ≡ 456 mod 7, 11, or 13.)

Answer

What I can do if I have understood well the question is the clear

$$12345678=949667\cdot13+\color{red}7=1122334\cdot11+\color{red}4=1763668\cdot7+\color{red}2$$ where the asked residues are in red.