Random Puzzles 

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
There are at least 13 in total.

Answer
There are at least 12 to choose from:

Ape, ewe, cat, kid, doe, fox, ox, kea, nag, ram, pig, cow.

Workings

Hint
The first letters of the words are: R, W, T, W, T.

Answer
Typewriter.

Rip, wet, tire, wire, try.

Workings

Hint
Where do they each grow?

Answer
Potato.

This is the only one that grows underground.