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Sum of divisors of 25 ·37 ·53 · 72 is –

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  1. 26 · 38 · 54 · 78    
  2. 26 · 38 · 54 · 73 – 2 · 3 · 5 · 7    
  3. 26 · 38 · 54 · 73 – 1    
  4. None of these    

    Answer:The correct answer is: None of theseAny divisor of 25 · 37 · 53 · 72 is of the type of 2l 3m 5n 7p, where 0less or equal than  l less or equal than 5, 0 less or equal thanless or equal than 7, 0  n  3 and 0 less or equal thanless or equal than 2
    Hence the sum of the divisors
    = (1 + 2 + …… + 25) (1 + 3 + ……. + 37) (1 + 5 + 52 + 53) (1 + 7 + 72)
    = open parentheses fraction numerator 2 to the power of 6 end exponent minus 1 over denominator 2 minus 1 end fraction close parentheses open parentheses fraction numerator 3 to the power of 8 end exponent minus 1 over denominator 3 minus 1 end fraction close parentheses open parentheses fraction numerator 5 to the power of 4 end exponent minus 1 over denominator 5 minus 1 end fraction close parentheses open parentheses fraction numerator 7 to the power of 3 end exponent minus 1 over denominator 7 minus 1 end fraction close parentheses
    =fraction numerator left parenthesis 2 to the power of 6 end exponent – 1 right parenthesis left parenthesis 3 to the power of 8 end exponent minus 1 right parenthesis left parenthesis 5 to the power of 4 end exponent minus 1 right parenthesis left parenthesis 7 to the power of 3 end exponent minus 1 right parenthesis over denominator 2 times 4 times 6 end fraction.

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