The product of $2×653×733×977$ has each digit exactly once except for one, which one is it? The product of $2×653×733×977$ is a number with nine digits and it contains every digit once except for one, which digit is that?

I noticed that it is a product of primes, but so far I cannot solve it without multiplying it out. I suspect I can solve this using modular arithmetic but I have no idea how. Any help?

In mod 9 we have
2*653*733*977 = 2*5*4*5 = 2 mod 9
Now we make the following table :
0+1+2+3+4+5+6+7+8+() = 36 = 0 mod 9
0+1+2+3+4+5+6+7+()+9 = 37 = 1 mod 9
0+1+2+3+4+5+6+()+8+9 = 38 = ...
0+1+2+3+4+5+()+7+8+9 = 39 = ...
0+1+2+3+4+()+6+7+8+9 = 40 = ...
0+1+2+3+()+5+6+7+8+9 = 41 = ...
0+1+2+()+4+5+6+7+8+9 = 42 = ...
0+1+()+3+4+5+6+7+8+9 = 43 = ...
0+()+2+3+4+5+6+7+8+9 = 44 = ...
()+1+2+3+4+5+6+7+8+9 = 45 = ...
After that, the missing number is .....
