180 (one hundred
ndeighty) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
179 and preceding
181.
In mathematics
180 is an
abundant number
In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total ...
, with its proper divisors summing up to 366.
180 is also the 11th
highly composite number
A highly composite number is a positive integer that has more divisors than all smaller positive integers. If ''d''(''n'') denotes the number of divisors of a positive integer ''n'', then a positive integer ''N'' is highly composite if ''d''(' ...
, a positive integer with 18 divisors, more than any smaller positive integer. One of the consequences of 180 having so many divisors is that it is a
practical number, meaning that any positive number smaller than 180 that is not a divisor of 180 can be expressed as the sum of some of 180's divisors. 180 is a Harshad number and a
refactorable number.
180 is the
sum of two
square number
In mathematics, a square number or perfect square is an integer that is the square (algebra), square of an integer; in other words, it is the multiplication, product of some integer with itself. For example, 9 is a square number, since it equals ...
s: 12
2 + 6
2. It can be expressed as either the sum of six consecutive
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
s:
19 +
23 +
29 +
31 +
37 +
41, or the sum of eight consecutive
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
s:
11 +
13 +
17 +
19 +
23 +
29 +
31 +
37. 180 is an
Ulam number
In mathematics, the Ulam numbers comprise an integer sequence devised by and named after Stanislaw Ulam, who introduced it in 1964. The standard Ulam sequence (the (1, 2)-Ulam sequence) starts with ''U''1 = 1 and ''U''2 =&nbs ...
, which can be expressed as a sum of earlier terms in the Ulam sequence only as 177 + 3.
180 is a 61-
gonal number,
[ while 61 is the 18th prime number.
Half a ]circle
A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ...
has 180 degrees,U-turn
A U-turn in driving refers to performing a 180° rotation to reverse the direction of travel. It is called a "U-turn" because the maneuver looks like the U, letter U. In some areas, the maneuver is illegal, while in others, it is treated as ...
is also referred to as a ''180''.
Summing Euler's totient function
In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In ot ...
φ(''x'') over the first + 24 integers gives 180.
In binary
Binary may refer to:
Science and technology Mathematics
* Binary number, a representation of numbers using only two values (0 and 1) for each digit
* Binary function, a function that takes two arguments
* Binary operation, a mathematical op ...
it is a digitally balanced number, since its binary representation has the same number of zeros as ones (10110100).
A triangle
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...
has three interior angles that collectively total 180 degrees. In general, the interior angles of an -sided polygon add to degrees.
References
External links
*
*
{{DEFAULTSORT:180 (Number)
Integers