Largest 4-Digit Number Identification

The greatest number of 4 digits is 9999.

Divisibility Calculation

We need to find the smallest positive number to add to 9999 so that the sum is exactly divisible by 307.

First, divide 9999 by 307 to find the remainder:

$ 9999 \div 307 $

Performing the division:

$ 9999 = 307 \times 32 + 175 $

The remainder is 175.

Number to Add Determination

For the sum $9999 + x$ to be exactly divisible by 307, the remainder 175 needs to be increased to the next multiple of 307. The next multiple of 307 after 9999 is $307 * 33$.

Alternatively, we need $175 + x$ to be the next multiple of 307, which is 307.

Set up the equation:

$ 175 + x = 307 $

Solve for $x$:

$ x = 307 - 175 $

$ x = 132 $

Therefore, the smallest positive number that must be added is 132.