72 (number)

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).

← 71 72 73 →
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Cardinalseventy-two
Ordinal72nd
(seventy-second)
Factorization23 × 32
Divisors1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Greek numeralΟΒ´
Roman numeralLXXII
Binary10010002
Ternary22003
Octal1108
Duodecimal6012
Hexadecimal4816

In mathematics

Seventy-two is the sum of four consecutive primes (13 + 17 + 19 + 23), as well as the sum of six consecutive primes (5 + 7 + 11 + 13 + 17 + 19). The product of 8 and 9, 72 is a pronic number. The sum of Euler's totient function φ(x) over the first fifteen integers is 72. There are 17 solutions to the equation φ(x) = 72, more than any integer below 72, making it a highly totient number.

72 is the smallest number whose fifth power is the sum of five smaller fifth powers: 195 + 435 + 465 + 475 + 675 = 725.

The sum of the eighth row of Lozanić's triangle is 72.

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

In base 10, the number 72 is a Harshad number.

In maths and economics, 72 plays a role in the Rule of 72.

In science

In astronomy

In religion
  • 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 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 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.[1]
  • The good god Osiris was enclosed in a coffin by 72 evil disciples and accomplices of Set.[2]
  • 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).[3][4]
  • The number of demons sealed away by King Solomon with The Lesser Key of Solomon.

In other fields
See also: List of highways numbered 72

Seventy-two is also:

In sports and games
  • 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, which was at the time the National Basketball Association record.
  • The number of spaces in a game of Parcheesi, from start space to "home."

Footnotes
  1. ISBN 0-292-72076-9
  2. "Egyptian Myths", George Hart, p41, University of Texas Press, 1990
  3. "Sects In Islam - 73 Groups in Islam, Division - Denominations". Archived from the original on 6 May 2013. Retrieved 24 March 2013.
  4. 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"
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