 ## 31 Dec Some Interesting Properties of the Number 2016

We look at some interesting properties of the number $2016$. We mention in passing that the year $2016$ is a leap year.

1. The number factors as $2016=2^5\times 3^2\times 7$.
2. From the factorisation a lot of interesting observations can be made. Such as $16$ divides $2016$. The previous number where the number formed by its last two digits divide it was $2010$ and the next such number would be $2020$.
3. $2016$ can be written as $\binom{64}{2}$. Thus, number of ways of choosing two different squares from a chessboard is $2016$.
4. $2016$ is also the sixty-third triangular number.
5. $2016$ is divisible by all single digit positive integers other than $5$.
6. $2016$ in binary base looks like $11111100000$ and hence, $2016 = 2^5+2^6+2^7+2^8+2^9+2^{10}$
7. $2016$ is one less than a prime number and five more than another prime number.

For more interesting properties visit the On-Line Encyclopedia of Integer Sequences and search for 2016 to see lots of interesting sequences which contain 2016.

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