Find the sum of all the co-primes to 2016 which are less than 2016

552108

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5016

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558432

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580608

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Solution

The correct option is D $580608$
Prime factorization of $2016 = 2^{5} \times 3^{2} \times 7^{1}$
Number of coprimes which are less than that of $2016$
$2016 (1 - \frac{1}{2}) (1 - \frac{1}{3}) (1 - \frac{1}{7})$
$= 2016 \times \frac{1}{2} \times \frac{2}{3} \times \frac{6}{7} = 576$
Sum of co-primes of the $N = (N u m b e r o f c o p r i m e s) \times \frac{(N u m b e r)}{2} = 576 \times \frac{2016}{2} = 5, 80, 608$

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Which of the following is/are false?

$i . {(1)}^{2016} > {(1)}^{2014}$

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