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 dozen (i.e., half a "100" in duodecimal).


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.
  • The sum of the eighth row of Lozanić's triangle is 72.
  • In normal space, the exterior angles of an equilateral pentagon measure 72 degrees each.
  • 72 is a Harshad number.

[edit] In science

[edit] In astronomy

[edit] In religion

[edit] In other fields

Seventy-two is also: