65536 (number)

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655356553665537
Cardinalsixty-five thousand five hundred thirty-six
Ordinal65536th
(sixty-five thousand five hundred and thirty-sixth)
Factorization216
Divisors17 total
Roman numeralLXVDXXXVI
Binary100000000000000002
Ternary100222200213
Quaternary1000000004
Quinary40441215
Senary12232246
Octal2000008
Duodecimal31B1412
Hexadecimal1000016
Vigesimal83GG20
Base 361EKG36
 
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655356553665537
Cardinalsixty-five thousand five hundred thirty-six
Ordinal65536th
(sixty-five thousand five hundred and thirty-sixth)
Factorization216
Divisors17 total
Roman numeralLXVDXXXVI
Binary100000000000000002
Ternary100222200213
Quaternary1000000004
Quinary40441215
Senary12232246
Octal2000008
Duodecimal31B1412
Hexadecimal1000016
Vigesimal83GG20
Base 361EKG36

65536 is the natural number following 65535 and preceding 65537.

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

65536 is the smallest number with exactly 17 divisors.[1]

In mathematics[edit]

65536 is 2^{2^{2^{2}}}, so in tetration notation 65536 is ^42.

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

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

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.[3]

65536 is the largest known number such that the sum of its unitary divisors is prime (1 + 65536 = 65537, which is prime).[4]

In computing[edit]

65536 (216) is the number of different values representable in a number of 16 binary digits, also known as a short integer in many computer programming systems. Therefore,

In popular culture[edit]

There are 65536 different charts in Western geomancy.

References[edit]