Compute $(235432_7 \cdot 2551_7) \pmod{311_7} = N_7 = ?$ This is for my assembly language class. I am finding different answers. My answer was $15_7$. But a friend got 2824. Can someone please explain the correct way to do it if $15_7$ is wrong?
$$(235432_7 \cdot 2551_7) \pmod{311_7} = N_7 = ?$$

$235432$ in base 7 is $2+3\cdot 7 + 4\cdot 7^2+5\cdot 7^3+3\cdot 7^4+2\cdot 7^5 = 42751$ in base 10
$2551$ in base 7 is $1+5\cdot 7+5\cdot 7^2+2\cdot 7^3 = 967$ in base 10
$311$ in base 7 is $1+1\cdot 7 + 3\cdot 7^2 = 155$ in base 10
$42751\cdot 967\pmod{155}\equiv 12$
$12$ in decimal is $5+1\cdot 7$ is $15$ in base 7

Note, if the answer was expected to be in base 7, then your friends answer of $2824$ doesn't even make sense since $8$ is not a valid digit in base 7.
