150 (number)

← 149 150 151 →
← 150 151 152 153 154 155 156 157 158 159 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
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

• 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

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

1. "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
2. "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.