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

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

Integers

Sum of divisors

Exponents

But try the problem first...

Answer: 6045

Source

Suggested Reading

B.Stat Objective Problem 99

Challenges and Thrills of Pre-College Mathematics by University Press

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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