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353 has primitive roots because it is a Prime number. (Not all numbers have primitive roots) It has 160 primitive roots. Generally however when we talk about THE primitive root we are talking about the lowest. So, starting at 2,3,4,5, ...... create a spreadsheet where the columns are the numbers being tested and the rows contain the powers of these numbers modulo 353 up to 176 (=352/2).

The first column not containing a 1. is the lowest primitive root.

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Q: How do you find the primitive root of 353?
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