find the total number of prime factors 2^17×6^31×7^5×10^11×11^10×323^23
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Answer:
162
Distinct = 7
Step-by-step explanation:
Find the total number of prime factors 2^17×6^31×7^5×10^11×11^10×323^23
2¹⁷ * 6³¹ * 7⁵ * 10¹¹ * 11¹⁰ * 323²³
= 2¹⁷ * (2*3)³¹ * 7⁵ * (2*5)¹¹ * 11¹⁰ * (17*19)²³
= 2¹⁷ * 2³¹*3³¹ * 7⁵ * 2¹¹*5¹¹ * 11¹⁰ * 17²³*19²³
= 2⁵⁹ * 3³¹ * 7⁵ *5¹¹ * 11¹⁰ * 17²³ * 19²³
= 2⁵⁹ * 3³¹ *5¹¹ * 7⁵ * 11¹⁰ * 17²³ * 19²³
Distinct Prime Factor = 7 ( 2 , 3 , 5 , 7 , 11 , 17 , 19)
Total number of prime factors = 59 + 31 + 11 + 5 + 10 + 23 + 23 = 162
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