Multiplicative persistence: multiply digits until single digit. 679→6·7·9=378→3·7·8=168→1·6·8=48→4·8=32→3·2=6. That's 5 steps. Maximum known: 11 steps (277777788888899). Sloane conjectures no number ever needs more than 11.
How to Use
Enter a number:
- Chain: Full product sequence
- Steps: Persistence count
- Digits: Breakdown at each step
Persistence Records
Smallest numbers with each persistence: 0→0, 10→1, 25→2, 39→3, 77→4, 679→5, 6788→6, 68889→7, 2677889→8, 26888999→9, 3778888999→10, 277777788888899→11.
The Zero Trap
Any number with a 0 digit has persistence 1 (product=0, then 0 is single-digit). Numbers with many 1s don't help persistence either. So high-persistence numbers avoid 0s and 1s in their digits.
Step-by-Step Instructions
- 1Enter number.
- 2Multiply digits.
- 3Continue to single digit.
- 4Count steps.
- 5Compare records.