Math, asked by supriya45511203, 11 months ago

find the total number of prime factors 2^17×6^31×7^5×10^11×11^10×323^23​

Answers

Answered by amitnrw
10

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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