150 (number)
| ||||
|---|---|---|---|---|
| Cardinal | one hundred fifty | |||
| Ordinal | 150th (one hundred fiftieth) | |||
| Factorization | 2 × 3 × 52 | |||
| Divisors | 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 | |||
| Greek numeral | ΡΝ´ | |||
| Roman numeral | CL, cl | |||
| Binary | 100101102 | |||
| Ternary | 121203 | |||
| Senary | 4106 | |||
| Octal | 2268 | |||
| Duodecimal | 10612 | |||
| Hexadecimal | 9616 | |||
150 (one hundred [and] fifty) is the natural number following 149 and preceding 151.
In mathematics
[edit]- 150 is the sum of eight consecutive primes (7 + 11 + 13 + 17 + 19 + 23 + 29 + 31). Given 150, the Mertens function returns 0.[1]
- 150 is conjectured to be the only minimal difference greater than 1 of any increasing arithmetic progression of n primes (in this case, n = 7) that is not a primorial (a product of the first m primes).[2]
- The sum of Euler's totient function φ(x) over the first twenty-two integers is 150.
- 150 is a Harshad number and an abundant number.
- 150 degrees is the measure of the internal angle of a regular dodecagon.
In other fields
[edit]150 is also:
- The number of degrees in the quincunx astrological aspect explored by Johannes Kepler.
- The approximate value for Dunbar's number, a theoretical value with implications in sociology and anthropology. It is actually 148.
References
[edit]- ^ "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
- ^ "Sloane's A123556: Minimal difference of any increasing arithmetic progression of n primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-06-30.
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