The greatest 4-digit number exactly divisible by 70 is 9940.
To find this, we can divide the largest 4-digit number, 9999, by 70.
9999 ÷ 70 = 142.84...
Since we need a whole number for exact divisibility, we take the integer part of the result, which is 142.
Now, we multiply 142 by 70:
142 × 70 = 9940
Therefore, 9940 is the largest 4-digit number that is exactly divisible by 70.