Multiplicative Persistence

Replace an integer by the product of its decimal digits. Repeat until only one digit remains. The number of replacements is its multiplicative persistence. The final digit is a different result: two numbers can have the same final digit but require different numbers of steps. This experiment keeps the complete chain beside a selected digit multiplication so you can check both.

Check the chain with the actual controls

Open the Multiplicative Persistence experiment. These steps use its exact decimal inputs and button names.

1. Enter 487 in Starting number. Persistence is 3 and Final digit is 6. The selected iteration resets to 0, displaying current number 487 and next product 224.
2. Set Iteration to 1. Read 224, its factors 2 × 2 × 4 and the next product 16. Press Next to read 16 and its next product 6.
3. Press Finish. Selected iteration is 3 and current number is 6. Next product shows a dash because the single-digit stopping state has no further counted multiplication. Next and Finish are disabled.
4. Press Previous to return to iteration 2, or select Select step 1 in the ledger to inspect 224 again. Total Persistence remains 3 throughout.
5. Change Starting number to 105. Selection returns to iteration 0. Its digit factors include zero, so the next product is 0 and Persistence is 1. Compare starting directly at 0, whose Persistence is 0.
6. Enter 000487. The text keeps its leading zeros, while Canonical starting number is 487 and the three-step chain is unchanged. The module treats the input as an integer, rather than multiplying padding characters.
7. Press Reset experiment. Starting number returns to 679, selected iteration to 0, current number to 679 and next product to 378. The complete default chain has Persistence 5 and Final digit 6.