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What is the sum of all the factors of factorial 30?

8 Answers

62
Lokesh Verma ·

Hint: try to write 30! as 2a3b5c7d11e13f17g19h23i29j

The important thing is dont get scared seeing this expression :D

g=h=i=j=1 (trivially?)
a = 15+7+3+1 = 26
b = 10+3+1 = 14
c = 6+1 = 7
d = 4
e = 2

now find the sum of all factors of this number?

1
xYz ·

prime factorising 30!
226*314*57*74*112*132*17*19*23*29.....edited

62
Lokesh Verma ·

I think there is a mistake with the power of 3

1
xYz ·

and then sum of all divisors =(1+2+22.....+226)(1+3+32...+312)(......)(1+29)

62
Lokesh Verma ·

you still sure karna?

1
xYz ·

we have to subtract....some cases which give 1 and that number itself

62
Lokesh Verma ·

no karna..

i meant that you have to divide by (2-1), (3-1), (5-1) and so on [3]

106
Asish Mahapatra ·

226.314.57.74.112.132.17.19.23.29

sum of all divisors = (20+..+226)(30+..+314)...(230+23)(290+29)

nishant sir, karna's answer seems perfectly fine except for the power of 3 in #6

we need to divide by (2-1)(3-1)... only when we apply the GP formula for sum.. He has written the previous step

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