720 (number)

← 719 720 721 →
List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	seven hundred twenty
Ordinal	720th (seven hundred twentieth)
Factorization	2^4 × 3^2 × 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

720 is:

• 6! (6 factorial).
• a composite number with 30 divisors, more than any number below, making it a 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

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, N. J. A. (ed.). "Sequence A002182 (Highly composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. 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.
3. 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.
4. Wells, David (1987). The Penguin Dictionary of Curious and Interesting Numbers. London: Penguin Books. p. 719.
5. 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.