Find the sum of all positive factors of 1000000.
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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}
Exactly !!
it should be 496062
1000000= ( 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 ) = 2480437
Number of factors = 49
w e w i l l u s e t h e f o r m u l a p − 1 p n + 1 − 1 × q − 1 q k − 1 w h e r e n = 6 k = 6 p = 2 q = 5
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The sum = ∑ i = 0 6 2 i × ∑ i = 0 6 5 i = 2 4 8 0 4 3 7