36 (number)

Last updated
35 36 37
Cardinal thirty-six
Ordinal 36th
(thirty-sixth)
Factorization 22 × 32
Divisors 1, 2, 3, 4, 6, 9, 12, 18, 36
Greek numeral ΛϚ´
Roman numeral XXXVI
Binary 1001002
Ternary 11003
Senary 1006
Octal 448
Duodecimal 3012
Hexadecimal 2416

36 (thirty-six) is the natural number following 35 and preceding 37.

Contents

In mathematics

36 depicted as a triangular number and as a square number Square triangular number 36.svg
36 depicted as a triangular number and as a square number
36 as the sum of the first positive cubes Cube-sum-36.png
36 as the sum of the first positive cubes

36 is both the square of six, and the eighth triangular number [1] or the sum of the first eight non-zero positive integers, which makes 36 the first non-trivial square triangular number. [2] Aside from being the smallest square triangular number other than 1, it is also the only triangular number (other than 1) whose square root is also a triangular number. 36 is also the eighth refactorable number, as it has exactly nine positive divisors, and 9 is one of them; [3] in fact, it is the smallest positive integer with at least nine divisors, which leads 36 to be the 7th highly composite number. [4] It is the sum of the fourth pair of twin-primes (17 + 19), [5] and the 18th Harshad number in decimal, as it is divisible by the sum of its digits (9). [6]

It is the smallest number with exactly eight solutions (37, 57, 63, 74, 76, 108, 114, 126) to the Euler totient function . Adding up some subsets of its divisors (e.g., 6, 12, and 18) gives 36; hence, it is also the eighth semiperfect number. [7]

This number is the sum of the cubes of the first three positive integers and also the product of the squares of the first three positive integers.

36 is the number of degrees in the interior angle of each tip of a regular pentagram.

The thirty-six officers problem is a mathematical puzzle with no solution. [8]

The number of possible outcomes (not summed) in the roll of two distinct dice.

36 is the largest numeric base that some computer systems support because it exhausts the numerals, 0–9, and the letters, A-Z. See Base 36.

The truncated cube and the truncated octahedron are Archimedean solids with 36 edges. [9]

The number of domino tilings of a 4×4 checkerboard is 36. [10]

Since it is possible to find sequences of 36 consecutive integers such that each inner member shares a factor with either the first or the last member, 36 is an Erdős–Woods number. [11]

The sum of the integers from 1 to 36 is 666 (see number of the beast).

36 is also a Tridecagonal number. [12]

Measurements

In science

In religion

In the arts, culture, and philosophy

In sports

In other fields

See also

Related Research Articles

21 (twenty-one) is the natural number following 20 and preceding 22.

70 (seventy) is the natural number following 69 and preceding 71.

72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or six dozen.

34 (thirty-four) is the natural number following 33 and preceding 35.

37 (thirty-seven) is the natural number following 36 and preceding 38.

104 is the natural number following 103 and preceding 105.

100 or one hundred is the natural number following 99 and preceding 101.

300 is the natural number following 299 and preceding 301.

<span class="mw-page-title-main">360 (number)</span> Natural number

360 is the natural number following 359 and preceding 361.

400 is the natural number following 399 and preceding 401.

180 is the natural number following 179 and preceding 181.

666 is the natural number following 665 and preceding 667.

500 is the natural number following 499 and preceding 501.

700 is the natural number following 699 and preceding 701.

600 is the natural number following 599 and preceding 601.

800 is the natural number following 799 and preceding 801.

135 is the natural number following 134 and preceding 136.

225 is the natural number following 224 and preceding 226.

240 is the natural number following 239 and preceding 241.

304 is the natural number following 303 and preceding 305.

References

  1. Sloane, N. J. A. (ed.). "SequenceA000217(Triangular numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-06-15.
  2. "Sloane's A001110 : Square triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  3. Sloane, N. J. A. (ed.). "SequenceA033950(Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-06-15.
  4. "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  5. Sloane, N. J. A. (ed.). "SequenceA001097(Twin primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-06-15.
  6. Sloane, N. J. A. (ed.). "SequenceA005349(Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-06-15.
  7. "Sloane's A005835 : Pseudoperfect (or semiperfect) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  8. Weisstein, Eric W. "36 Officer Problem". mathworld.wolfram.com. Retrieved 2020-08-21.
  9. Weisstein, Eric W. "Archimedean Solid". mathworld.wolfram.com. Retrieved 2020-08-21.
  10. Weisstein, Eric W. "Domino Tiling". mathworld.wolfram.com. Retrieved 2020-08-21.
  11. "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  12. Sloane, N. J. A. (ed.). "SequenceA051865(13-gonal (or tridecagonal) numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  13. 1 2 "How Many? A Dictionary of Units of Measurement. -Y". Archived from the original on 22 September 2007. Retrieved 2007-09-15.
  14. "WebElements.com – Krypton". Archived from the original on 4 August 2007. Retrieved 2007-08-13.
  15. "36bit.org". Archived from the original on 11 September 2007. Retrieved 2007-09-15.
  16. 1 2 3 4 Winston, Pinchas (1995). The Wonderful World of Thirty-six. Mercava Productions. ISBN   0-9698032-4-9.
  17. "The Creation of Man". The Coming of the Maori. Retrieved 2016-04-24.
  18. Betz, Hans Dieter (1996). The Greek Magical Papyri in Translation. University of Chicago Press. ISBN   9780226044477.
  19. "Adelaide 36ers Homepage". Archived from the original on 11 August 2007. Retrieved 13 August 2007.