72 (number)

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← 71 72 73 →
Cardinal seventy-two
Ordinal 72nd
Factorization 23× 32
Divisors 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Roman numeral LXXII
Binary 10010002
Ternary 22003
Quaternary 10204
Quinary 2425
Senary 2006
Octal 1108
Duodecimal 6012
Hexadecimal 4816
Vigesimal 3C20
Base 36 2036

72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or 6 dozen (i.e., 60 in duodecimal).

In mathematics[edit]

72 is:

  • the sum of four consecutive primes (13 + 17 + 19 + 23).
  • the sum of six consecutive primes (5 + 7 + 11 + 13 + 17 + 19).
  • a pronic number, being the product of 8 and 9.[1]
  • the smallest number whose fifth power is the sum of five smaller fifth powers: 195 + 435 + 465 + 475 + 675 = 725.
  • a palindromic number in bases 5 (2425), 11 (6611), 17 (4417), 23 (3323) and 35 (2235).
  • a Harshad number in bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 and 16.
  • the sum of the eighth row of Lozanić's triangle.
  • the sum of Euler's totient function φ(x) over the first fifteen integers.
  • a highly totient number because there are 17 solutions to the equation φ(x) = 72, more than any integer below 72.[2]

In a plane, the exterior angles of a regular pentagon measure 72 degrees each.

In science[edit]

In astronomy[edit]

In religion[edit]

  • The number of languages spoken at the Tower of Babylon, according to later tradition.
  • The conventional number of scholars translating the Septuagint, according to the legendary account in the "Letter of Aristeas".
  • The conventional number of disciples sent forth by Jesus in Luke 10 in some manuscripts (seventy in others).
  • The number of names of God, according to Kabbalah (see names of God in Judaism).
  • The Shemhamphorasch related to the number of the names of God.
  • The total number of books in the Holy Bible in the Catholic version if the Book of Lamentations is considered part of the Book of Jeremiah.
  • The current distribution of the Book of Revelation is 22 chapters, adopted since the 13th century, but the oldest known division of the text is that of the Greek commentator Andrew of Cesary (6th century) in 72 chapters.
  • The number of people martyred along with Imam Hussain at the Battle of Karbala.
  • The number of soldiers who will fight alongside Imam Mahdi against the Dajjal, according to Islamic ahadith are 313 not 72.
  • The 72 old men of the synagogue, according to the Zohar.
  • The number of houri each Muslim martyr (or every Muslim male, according to some ahadith) shall receive as companions in Paradise.
  • The degrees of the Jacob's Ladder were to the number of 72, according to the Zohar.
  • The 72 disciples of Confucius who mastered his teachings (also given as 77).
  • Mahavira, the twenty-fourth and last tirthankara of Jainism, is said to have attained nirvana after his physical death at the age of 72.
  • Thoth, in an Egyptian creation myth, wins a 72nd of each day of the year from the Moon in a game of draughts, as a favour to Nut, the Sky Goddess. He uses these portions to make the five intercalary days on which the remaining Gods and Goddesses are born.[3]
  • The good god Osiris was enclosed in a coffin by 72 evil disciples and accomplices of Set.[4]
  • At the age of the puberty, the young Parsee received the investiture of the sacred cord Kucti made of 72 linens in symbol of the community.
  • In Cao Đài, the number of planets between hell and heaven.
  • There are 72 stupas which comprise Borobudur, the world’s largest Buddhist temple.
  • 72 major temples have been found at Angkor, seat of the ancient Khmer Empire.
  • In Islam, 72 is the number of sects or denominations that are doomed to Hell, according to Hadith (Sayings of prophet Muhammad).[5][6]
  • ezidi refer to 72 nations.[7]
  • Lists of 72 different names for Jerusalem have been compiled from Jewish Scripture.
  • There are 72 demons and other spirits in the goetia The Lesser Key of Solomon.
  • 72 men along side with Imam Hussein fought against Yazid in Karbala.

In other fields[edit]

Seventy-two is also:

In sports and games[edit]

  • The usual par for an 18 hole golf course, especially those in tournament play.
  • The number of victories the Chicago Bulls achieved during the 1995-96 NBA season
  • The number of spaces in a game of Parcheesi, from start space to "home."

In Software[edit]

  • Older SAP systems allowed only 72 characters of length in the source code .


Harald Specht: “Der Jahwe-Code – Auf den Spuren der heiligen Zahl 72”, Leipzig 2011, ISBN 978-3-86268-375-8.


  1. ^ "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29. 
  2. ^ "Sloane's A097942 : Highly totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29. 
  3. ^ ISBN 0-292-72076-9
  4. ^ "Egyptian Myths", George Hart, p41, University of Texas Press, 1990
  5. ^ "Sects In Islam - 73 Groups in Islam, Division - Denominations". Retrieved 24 March 2013. 
  6. ^ Sunan Ibn Maajah, no. 3982 "My Ummah will be divided into seventy-three sects, one of which will be in Paradise and seventy-two will be in the Fire"
  7. ^ http://www.telesurtv.net/english/opinion/An-End-to-the-Yazidi-Tragedy-Only-Comes-with-Kurdish-Freedom-20151220-0004.html

External links[edit]