72 (number)

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72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or 6 dozens (i.e., half a "100" in duodecimal).


<< 70 71 72 73 74 75 76 77 78 79 >>

Cardinal 72
seventy-two
Ordinal 72nd
seventy-second
Factorization 2^3 \cdot 3^2
Divisors 1, 2, 3, 4, 6, 8, 9,
12, 18, 24, 36, 72
Roman numeral LXXII
Binary 1001000
Duodecimal 60
Hexadecimal 48

Contents

[edit] 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. And as a multiple of a perfect number, 72 is itself a semiperfect 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.

In normal space, the exterior angles of an equilateral pentagon measure 72 degrees each.

72 is a Harshad number

[edit] In science

In astronomy,

Messier object M72, a magnitude 10.0 globular cluster in the constellation Aquarius
The New General Catalogue object NGC 72, a magnitude 13.5 barred spiral galaxy in the constellation Andromeda
The Saros number of the solar eclipse series which began on -727 August 16 and ended on 752 January 21. The duration of Saros series 72 was 1478.1 years, and it contained 83 solar eclipses.
The Saros number of the lunar eclipse series which began on -407 June 5 and ended on 891 July 25. The duration of Saros series 72 was 1298.1 years, and it contained 73 lunar eclipses.

[edit] In religion

  • 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 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 number of heavenly virgins (Hour Al-Aeen) Muslim martyrs are promised to get in heaven by their recruiters.

[edit] In other fields

Seventy-two is also: