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

8 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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