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June 14, 2020

Sum of divisors and Integers | TOMATO B.Stat Objective 99

Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Sum of divisors and Integers.

Sum of divisors and Integers (B.Stat Objective Question)

The sum of all positive divisors of 1800, where 1 and 1800 are also considered as divisors of 1800, is

  • 104
  • 6045
  • 1154
  • none of these

Key Concepts


Integers

Sum of divisors

Exponents

Check the Answer


Answer: 6045

B.Stat Objective Problem 99

Challenges and Thrills of Pre-College Mathematics by University Press

Try with Hints


First hint

here 1800=(2)(2)(2)(3)(3)(5)(5) where n=\((p_1^a)(p_2^b)(p_3^c)\)

Second Hint

sum of divisors of 1800

=\((\frac{2^{4}-1}{2-1})\)\((\frac{3^{3}-1}{3-1})\)\((\frac{5^{3}-1}{5-1})\) where sum of divisors of n=\((\frac{p_1^{a+1}-1}{p_1-1})(\frac{p_2^{b+1}-1}{p_2-1})(\frac{p_3^{c+1}-1}{p_3-1})\)

Final Step

=6045.

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