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Workings

Answer
This puzzle is a classic paradox. You can wrangle with the logic for hours and never reach an absolute conclusion.

Workings

Hint
Try starting with the cube root of the number.

Answer
195 x 197 x 199.

Reasoning
Since we're after three numbers that multiply together, a good place to start is the cube root of 7,644,585, which is roughly 196.99.

Let's try dividing by the closest odd number to 196.99:

   7644585 ÷ 197 = 38805

We're now after whole divisors of 38,805, so trying either odd number either side of 197 might work.

Trying either 195 or 199 gives the answer.

Double-Checking
   195 x 197 x 199 = 7,644,585

Note
Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.

Workings

Hint
A very common sequence, but in base 8!

Answer
13.

Odd numbers expressed in base 8, 11 in base 8 = 13.

Workings

Hint
Think of Roman numerals.

Answer
Delta.

Take the Roman numerals in sequence, and convert to the phonetic alphabet.
  1 = I = India
  5 = V = Victor
 10 = X = X-Ray
 50 = L = Lima
100 = C = Charlie
500 = D = Delta