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.

References :

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Bishal Deb

Bishal Deb is an undergraduate student at Chennai Mathematical Institute. He is an editor of Gonit Sora.

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