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
here 1800=(2)(2)(2)(3)(3)(5)(5) where n=\((p_1^a)(p_2^b)(p_3^c)\)
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=\((\frac{p_1^{a+1}-1}{p_1-1})(\frac{p_2^{b+1}-1}{p_2-1})(\frac{p_3^{c+1}-1}{p_3-1})\)
\(=(2)^{10}(49)(47)(15)(43)(41)(13)(37)(35)(11)(31)(29)\times \frac{1}{(12)(11)(10)(8)(7)(5)(4)(1)}[(2)(9)]\)gives a factor of \((18)^{1}\) then highest power of 18 is 1.
