720 (number)

From HandWiki
Short description: Natural number
← 719 720 721 →
Cardinalseven hundred twenty
Ordinal720th
(seven hundred twentieth)
Factorization24 × 32 × 5
Divisors1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
Greek numeralΨΚ´
Roman numeralDCCXX
Binary10110100002
Ternary2222003
Quaternary231004
Quinary103405
Senary32006
Octal13208
Duodecimal50012
Hexadecimal2D016
Vigesimal1G020
Base 36K036

720 (seven hundred [and] twenty) is the natural number following 719 and preceding 721.

It is 6! (6 factorial) and a composite number with thirty divisors, more than any number below, making it a highly composite number.[1] It is a Harshad number in every base from binary to decimal.

720 is expressible as the product of consecutive integers in two different ways: 720 = 1 × 2 × 3 × 4 × 5 × 6 and 720 = 8 × 9 × 10. [2]

There are 49 solutions to the equation φ(x) = 720, more than any integer below it, making 720 a highly totient number.

720 is a 241-gonal number.

In other fields

720 is:

  • A common vertical display resolution for HDTV (see 720p).
  • 720° is two full rotations; the term "720" refers to a skateboarding trick.
  • 720° is also the name of a skateboarding video game.
  • 720 is a dual area code in the Denver Metro Area along with 303.
  • 720° is the sum of all the defects of any polyhedron.
  • 720 is a short form of saying Boeing 720, an airliner which is no longer in service.

For the year AD, see 720.

References

  1. "Sloane's A002182 : Highly composite numbers". OEIS Foundation. https://oeis.org/A002182. 
  2. Wells, David (1987). The Penguin Dictionary of Curious and Interesting Numbers. London: Penguin Books. pp. 719.