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How many positive factors are there of the number 360 and find the sum of all these factors.

How many positive factors are there of the number 360 and find the sum of all these factors.

Grade:11

1 Answers

sanatan sharma
26 Points
9 years ago

360 = 62.5.2

360 = 23.32.5

therefore no of factors = (3+1)(2+1)(1+1) = 24

this  comes as  i can take  2  : none i.e 1 , one two =2 , two two''s (22)=4 , three two''s(23) = 8

and same for the other primes also  

sum of all the factors = (20+21+22+23 )(30+31+32)(50+51)

if you see carefully the above expression represents sum of all the factors 

  like      20.30.50 =1 

and     23.32.51 = 360 

now apply individual sum of G.P. formula for the 3 brackets and obtain the answer 

 

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