720 (number)
| ||||
|---|---|---|---|---|
| Cardinal | seven hundred twenty | |||
| Ordinal | 720th (seven hundred twentieth) | |||
| Factorization | 24 × 32 × 5 | |||
| Divisors | 1, 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 numeral | ΨΚ´ | |||
| Roman numeral | DCCXX | |||
| Binary | 10110100002 | |||
| Ternary | 2222003 | |||
| Senary | 32006 | |||
| Octal | 13208 | |||
| Duodecimal | 50012 | |||
| Hexadecimal | 2D016 | |||
720 (seven hundred [and] twenty) is the natural number following 719 and preceding 721.
In mathematics
[edit]720 is:
- 6! (6 factorial).
- a composite number with 30 divisors, more than any number below, making it the 14th highly composite number.[1]
- a highly abundant number.[2]
- a Harshad number in every base from binary to decimal.
- the smallest number to be palindromic in 16 bases.[3]
- a 241-gonal number.
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.[4]
There are 49 solutions to the equation φ(x) = 720, more than any integer below it, making 720 a highly totient number.[5]
In other fields
[edit]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
[edit]- ^ Sloane, N. J. A. (ed.). "Sequence A002182 (Highly composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002093 (Highly abundant numbers: numbers k such that sigma(k) > sigma(m) for all m < k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A037183 (Smallest number that is palindromic (with at least 2 digits) in n bases)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Wells, David (1987). The Penguin Dictionary of Curious and Interesting Numbers. London: Penguin Books. p. 719.
- ^ Sloane, N. J. A. (ed.). "Sequence A097942 (Highly totient numbers: each number k on this list has more solutions to the equation phi(x) = k than any preceding k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.