| ||||
|---|---|---|---|---|
| Cardinal | one hundred eighty | |||
| Ordinal | 180th (one hundred eightieth) | |||
| Factorization | 22 × 32 × 5 | |||
| Divisors | 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 | |||
| Greek numeral | ΡΠ´ | |||
| Roman numeral | CLXXX | |||
| Binary | 101101002 | |||
| Ternary | 202003 | |||
| Octal | 2648 | |||
| Duodecimal | 13012 | |||
| Hexadecimal | B416 | |||
180 (one hundred [and] eighty) is the natural number following 179 and preceding 181.
In mathematics
180 is an abundant number, with its proper divisors summing up to 366.[1][2] 180 is also a highly composite number, a positive integer with more divisors 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 refactorable number.[3]
180 is the sum of two square numbers: 122 + 62. It can be expressed as either the sum of six consecutive prime numbers: 19 + 23 + 29 + 31 + 37 + 41, or the sum of eight consecutive prime numbers: 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37. 180 is an Ulam number, which can be expressed as a sum of earlier terms in the Ulam sequence only as 177 + 3.[4]
Half a circle has 180 degrees.[5]
Summing Euler's totient function φ(x) over the first + 24 integers gives 180.
180 is a Harshad number in base 10, and in binary it is a digitally balanced number, since its binary representation has the same number of zeros as ones (10110100).
In religion
The Book of Genesis says that Isaac died at the age of 180.[6]
See also
- List of highways numbered 180
- United Nations Security Council Resolution 180
- United States Supreme Court cases, Volume 180
- Pennsylvania House of Representatives, District 180
References
- ^ "Positive Integers: 180".
- ^ a b "The Number 180". VirtueScience.com.
- ^ "Refactorable numbers". On-Line Encyclopedia of Integer Sequences. The OEIS Foundation. 2016-04-18. Retrieved 2016-04-18.
- ^ "Ulam numbers". On-Line Encyclopedia of Integer Sequences. The OEIS Foundation. 2016-04-18. Retrieved 2016-04-18.
- ^ Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers. London: Penguin Group. p. 142. ISBN 0-14-026149-4.
- ^ Genesis 35:28–29
External links
- "180". The Number Dictionary.
- G. L. Honaker, Jr. "Prime curiosities: 180". UTM.