This year's divisors

What is the mean of all positive divisors of the number 2016?


The answer is 182.

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1 solution

Rishabh Jain
Feb 28, 2016

2016 = 2 5 × 3 2 × 7 \Large 2016=\color{#D61F06}{2^5\times 3^2\times 7} No. of divisors= ( 5 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 36 (5+1)(2+1)(1+1)=36
Sum of them= ( 2 0 + 2 1 + 2 2 + 2 3 + 2 4 + 2 5 ) ( 3 0 + 3 1 + 3 2 ) ( 7 0 + 7 1 ) = 6552 (2^0+2^1+2^2+2^3+2^4+2^5)(3^0+3^1+3^2)(7^0+7^1)=6552

Hence mean = 6552 36 = 182 \dfrac{6552}{36}=\large\boxed{\color{#20A900}{182}}

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