Sum of all factors!

Find the sum of all positive factors of 1000000.


The answer is 2480437.

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3 solutions

Mohamed Aly
Mar 27, 2014

The sum = i = 0 6 2 i × i = 0 6 5 i = 2480437 \sum_{i=0}^6 2^{i} \times \sum_{i=0}^6 5^{i} = \boxed{2480437}

I think it should be 496062 as 1000000=2^6+5^6 so required answer =1+2+4+6+8+16+32+64}{1+5+25+125+625+3125}

ashutosh mahapatra - 7 years, 2 months ago

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Its not 2^6 + 5^6, its multiplication

Kushagra Sahni - 7 years, 1 month ago

Exactly !!

Vishal Sharma - 7 years, 2 months ago

it should be 496062

Vishal Rockzz - 7 years ago
Ahmed Kamal
Jan 23, 2015

1000000= ( 2 2 2 2 2 2 ) ( 5 5 5 5 5 5 ) ( 1 (2*2*2*2*2*2)*(5*5*5*5*5*5)*(1 ). So,

The sum of all factors= ( y = 0 6 ( x = 0 6 2 x ) 5 y ) \left( \sum _{ y=0 }^{ 6 }{ \left( \sum _{ x=0 }^{ 6 }{ { 2 }^{ x } } \right) } { 5 }^{ y } \right) = 2480437

Number of factors = 49

Mehul Chaturvedi
Dec 13, 2014

w e w i l l u s e t h e f o r m u l a p n + 1 1 p 1 × q k 1 q 1 w h e r e n = 6 k = 6 p = 2 q = 5 we\quad will\quad use\quad the\quad formula\\ \\ \frac { p^{ n+1 }-1 }{ p-1 } \times \frac { { q }^{ k-1 } }{ q-1 } \\ where\quad n=6\quad k=6\\ p=2\quad q=5\\

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