Sorry, no online dictionaries contain the exact phrase varies based on many factors.
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Reverse dictionary results:
1. variable
 2. fluctuating
3. changeable
4. contingent
5. adaptable
6. persistency
7. versatile
8. discrete
9. stickability
10. apart
 11. deterministically
12. ephemerality
13. inseparate
14. likelihood
15. measurably
16. ongoingness
17. practicably
18. precision
19. separate
20. transiency
 21. accessible
22. adaptive
23. continuousness
24. equable
25. explicably
26. extendability
27. extensiveness
28. fugacity
29. hard coded
30. intervisible
 31. labile
32. noticeable
33. optimality
34. palpable
35. perceivable
36. permanence
37. perpetuity
38. persistence

You can look up the words in the phrase individually using these links:   varies ?   based ?   on ?   many ?   factors ?
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