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#42 Persistence
Set by Peter Rowlett
A number’s persistence is given by the steps needed to reach a single-digit whole number by repeatedly multiplying all its digits together. For 39, for example, we start with 3×9 to give 27, then 2×7 is 14 and 1×4 is 4. This took three steps, so the persistence of 39 is 3. We ended up with 4, so we say the root of 39 using this rule is 4.
What are the persistence and root of 77?
What is the smallest number with a persistence of 1?
What is the largest…
