Q20 / 98 · NTA Abhyas (JEE Main) 2020 · Mathematics · Permutation Combination

The sum of the divisors of $9600$ is

A
$3048$
B
$6120$
Correct answer
C
$31620$
D
$24384$

Solution

9600 = 96 \times 100 = 2^{7} \times 3^{1} \times 5^{2}

Number of divisors

= 8 \times 2 \times 3 = 48

Sum of divisors

= (2^{0} + 2^{1} + 2^{2} + . . . . . . . + 2^{7}) (3^{0} + 3^{1}) (5^{0} + 5^{1} + 5^{2})

= \frac{2^{8} - 1}{2 - 1} \times \frac{3^{2} - 1}{3 - 1} \times \frac{5^{3} - 1}{5 - 1}

= 255 \times \frac{8}{2} \times \frac{124}{4}

= 31620

Hence, the correct answer is option: 'C'.

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