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By prime factorization of 10101010101010101 we follow 5 simple steps:
1. We write number 10101010101010101 above a 2-column table
2. We divide 10101010101010101 by the smallest possible prime factor
3. We write down on the left side of the table the prime factor and next number to factorize on the ride side
4. We continue to factor in this fashion (we deal with odd numbers by trying small prime factors)
5. We continue until we reach 1 on the ride side of the table
| 10101010101010101 | |
| prime factors | number to factorize |
| 3 | 3367003367003367 |
| 3 | 1122334455667789 |
| 7 | 160333493666827 |
| 13 | 12333345666679 |
| 19 | 649123456141 |
| 37 | 17543877193 |
| 52579 | 333667 |
| 333667 | 1 |
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