Trisha Shetty (Editor)

65536 (number)

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65536
  
65537 →

Divisors
  
17 total

Factorization
  
2

Roman numeral
  
LXVDXXXVI

Cardinal
  
sixty-five thousand five hundred thirty-six

Ordinal
  
65536th (sixty-five thousand five hundred and thirty-sixth)

65536 is the natural number following 65535 and preceding 65537.

Contents

65536 is a power of two: 2 16 (2 to the 16th power).

65536 is the smallest number with exactly 17 divisors.

In mathematics

65536 is 2 2 2 2 , so in tetration notation 65536 is 4 2 .

When expressed using Knuth's up-arrow notation, 65536 is 2 ↑ 16 , which is equal to 2 ↑ 2 ↑ 2 ↑ 2 , which is equivalent to 2 ↑↑ 4 or 2 ↑↑↑ 3 .

65536 is a superperfect number - a number such that σ(σ(n))=2n.

A 16-bit number can distinguish 65536 different possibilities, such as the numbers 0..65535. In unsigned binary notation, 65536 is thus the smallest number that can not be represented by 16 bits.

65536 is the only power of 2 less than 231000 that does not contain the digits 1, 2, 4 or 8 in its decimal representation.

65536 is the largest known number such that the sum of its unitary divisors is prime (1 + 65536 = 65537, which is prime).

65536 is an untouchable number.

In computing

65536 (216) is the number of different values representable in a number of 16 binary digits (or bits), also known as an unsigned short integer in many computer programming systems. This can place a limitation on many common hardware and software implementations, some examples of which are:

  • The Motorola 68000 family, x86 architecture, and other computing platforms have a word size of 16 bits, representing 65536 possible values. (32- or 64-bit operations are supported equally or better in modern microprocessors.)
  • 65536 is the maximum number of spreadsheet rows supported by Excel 97, Excel 2000, Excel 2002 and Excel 2003.Text files that are larger than 65536 rows cannot be imported to these versions of Excel. (Excel 2007, 2010 and 2013 support 1,048,576 rows (220)).
  • A 16-bit microprocessor chip can directly access 65536 memory addresses, and the 16-bit highcolor graphics standard supports a color palette of 65536 different colors.
  • The maximum number of methods allowed in a single dex file Android application is 65536.
  • The limit for the amount of code in bytes for a non-native, non-abstract method in Java.

    • There are 65536 different charts in Western geomancy.

    References

    65536 (number) Wikipedia
    (Text) CC BY-SA