32 (number)

← 31 32 33 →
← 30 31 32 33 34 35 36 37 38 39 → List of numbers — Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	thirty-two
Ordinal	32nd (thirty-second)
Factorization	2^5
Divisors	1, 2, 4, 8, 16, 32
Roman numeral	XXXII
Binary	1000002
Ternary	10123
Quaternary	2004
Quinary	1125
Senary	526
Octal	408
Duodecimal	2812
Hexadecimal	2016
Vigesimal	1C20
Base 36	W36

32 (thirty-two) is the natural number following 31 and preceding 33.

In mathematics

32 is the smallest number n with exactly 7 solutions to the equation φ(x) = n. It is also the sum of the totient function for the first ten integers.

The fifth power of two, 32 is also a Leyland number since 2⁴ + 4² = 32.^[1]

As with every power of two, 32 has an aliquot sum one less than itself: the prime 31. 32 is the first member of the 31-aliquot tree.

32 is the ninth happy number.^[2]

32 = 1¹ + 2² + 3³

In science

• The atomic number of germanium
• The freezing point of water at sea level in degrees Fahrenheit

Astronomy

• Messier 32, a magnitude 9.0 galaxy in the constellation Andromeda which is a companion to M31.
• The New General Catalogue object NGC 32, a star in the constellation Pegasus
• The Saros number of the solar eclipse series which began on September 24, 1957 BC and ended on March 10, 460 BC. The duration of Saros series 32 was 1496.5 years, and it contained 84 solar eclipses.
• The Saros number of the lunar eclipse series which began on June 11, 1691 BC and ended on August 9, 375 BC. The duration of Saros series 32 was 1316.2 years, and it contained 74 lunar eclipses.

In music

• The number of completed, numbered piano sonatas by Ludwig van Beethoven
• In the title and lyrics of the song "32 Footsteps" by They Might Be Giants
• In the title of the song "The Chamber of 32 Doors" by Genesis, from their 1974 concept album The Lamb Lies Down On Broadway
• The title of "32", a song on Mr. Mister's debut album I Wear the Face
• The number of rays in the Japanese Rising Sun on the cover of Incubus' 2006 album Light Grenades
• The title of "32 Ways To Die", a song on Sum41's album Half Hour of Power
• The shortened pseudonym of UK rapper Wretch 32
• Thirty Two is the fourth album by English band Reverend and the Makers

In religion

In the Kabbalah, there are 32 Kabbalistic Paths of Wisdom.

One of the central texts of the Pāli Canon in the Theravada Buddhist tradition, the Digha Nikaya, describes the appearance of the historical Buddha with a list of 32 physical characteristics.

The Hindu scripture Mudgala Purana also describes Ganesha as taking 32 forms.

In sports

In chess, the total number of black squares on the board, the total number of white squares, and the total number of pieces (black and white) at the beginning of the game.

The jersey number 32 has been retired by several North American sports teams in honor of past playing greats:

• In Major League Baseball:
  • The Houston Astros, for Jim Umbricht.
  • The Los Angeles Dodgers, for Hall of Famer Sandy Koufax.
  • The New York Yankees, for Elston Howard.
  • The Philadelphia Phillies, for Hall of Famer Steve Carlton.
• In the NFL:
  • The Cleveland Browns, for Hall of Famer Jim Brown.
  • The New York Giants, for Al Blozis, who left the team to serve with the United States Army in World War II and was killed in action in 1945.
  • Although the Buffalo Bills have not officially retired #32, they have not issued it since Hall of Famer O. J. Simpson was traded from the team in 1977.
  • The Pittsburgh Steelers currently have a policy of not retiring numbers, having retired only one number (70) in their earlier history. However, the Steelers have not issued #32 since the retirement of Hall of Famer Franco Harris.
• In the NBA:
  • The Boston Celtics, for Hall of Famer Kevin McHale.
  • The Brooklyn Nets, for Hall of Famer Julius Erving, who played with the team when it was on Long Island as the New York Nets.
  • The Los Angeles Lakers, for Hall of Famer Magic Johnson.
  • The Milwaukee Bucks, for Brian Winters.
  • The Philadelphia 76ers, for Hall of Famer Billy Cunningham. The Sixers briefly took the number out of retirement with Cunningham's blessing to issue it to another future Hall of Famer, Charles Barkley.
  • The Portland Trail Blazers, for Hall of Famer Bill Walton.
  • The San Antonio Spurs, for Sean Elliott.
  • The Seattle SuperSonics, for Fred Brown. The team has since relocated to become the Oklahoma City Thunder, but the Thunder has yet to issue any of the numbers retired by the franchise in Seattle.
  • The Utah Jazz, for Hall of Famer Karl Malone.
• In the NHL:
  • The Washington Capitals, for Dale Hunter.

The number of teams in the National Football League.

The number of national teams that have participated in each FIFA World Cup finals tournament since 1998.

The ball used in association football is typically made with 32 panels of leather or synthetic material.

In other fields

Thirty-two could also refer to:

• The number of teeth of a full set of teeth in an adult human, including wisdom teeth
• The size of a databus in bits: 32-bit
• The size, in bits, of certain integer data types, used in computer representations of numbers
• IPv4 uses 32-bit (4-byte) addresses
• ASCII and Unicode code point for space
• The code for international direct dial phone calls to Belgium
• In the title Thirty-Two Short Films About Glenn Gould, starring Colm Feore
• Article 32 of the UCMJ concerns pre-trial investigations. Such a hearing is often called an "article 32 hearing"
• Sometimes considered to be the occult opposite of number 23
• The caliber .32 ACP
• The number of pages in the average comic book (not including the cover)
• The number of the French department Gers
• The traditional 32 counties of Ireland

References

• Prime Curios! 32 from the Prime Pages

1. "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
2. "Sloane's A007770 : Happy numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.