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We have to find total number of divisor of form $4n+2$ of the number $2016$.

My attempt:

$2016=2^53^27^1$

So total number of divisors is $6\times 3 \times 2=36$.

2 Answers 2

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$$(4n+2)|2016 \iff (2n+1)|1008$$ As $2n+1$ is odd, we need to find the number of odd divisors of $1008$. Note that this implies $$(2n+1)|63=3^2 \times 7$$ So the number of divisors are $(2+1)(1+1)-1=5$ as $2n+1>1$.

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    Answer is given as5 – 2017-02-12
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    @Koolman I edited my answer. – 2017-02-12
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As $4n+2=2(2n+1)$

So, we actually need the number of odd divisors which is $(2+1)(1+1)$

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    Answer is given as 5 – 2017-02-12
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    @Koolman, $$2X\{1,3,9\}X\{1,7\}=\{2,6,18,14,42,126\}$$ – 2017-02-12