A number's persistence is the number of steps required to reduce it to a single digit by multiplying all its digits to obtain a second number, then multiplying all the digits of that number to obtain a third number, and so on until a one-digit number is obtained.
For example, 66 has a persistence of three because it requires three steps to reduce it to one digit: 66-36-18-8.
*smacks forehead* Recursion makes a lot of sense here. Wish I had thought of it...
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