Averaging The Factors Of 2016

Find the average of all the factors of 2016.

As an explicit example, all the factors of 6 are 1, 2, 3 and 6. Thus the average of all the factors of 6 is ( 1 + 2 + 3 + 6 ) ÷ 4 = 3 (1+2+3+6)\div4 =3 .


The answer is 182.

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1 solution

Joel Yip
Feb 7, 2016

Firstly, 2016 = 2 5 × 3 2 × 7 2016={ 2 }^{ 5 }\times { 3 }^{ 2 }\times 7

So the number of factors is just 6 × 3 × 2 = 36 6 \times 3 \times 2=36

And the sum of factors is 2 6 1 2 1 × 3 3 1 3 1 × 7 2 1 7 1 = 6552 \frac { { 2 }^{ 6 }-1 }{ 2-1 } \times \frac { { 3 }^{ 3 }-1 }{ 3-1 } \times \frac { { 7 }^{ 2 }-1 }{ 7-1 } =6552

So the average is 6552 ÷ 36 = 182 6552\div 36=\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{182}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}

\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}

veri nais usage of box :-)

Vu Vincent - 3 years, 11 months ago

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