150 (number)

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← 149 150 151 →
Cardinalone hundred fifty
Ordinal150th
(one hundred fiftieth)
Factorization2 × 3 × 52
Divisors1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Greek numeralΡΝ´
Roman numeralCL
Binary100101102
Ternary121203
Octal2268
Duodecimal10612
Hexadecimal9616

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.

In the Bible[edit]

  • The last numbered Psalm in the Bible, Psalm 150, considered the one most often set to music.
  • The number of sons of Ulam, who were combat archers, in the Census of the men of Israel upon return from exile (I Chronicles 8:40)
  • In the Book of Genesis, the number of days the waters from the Great Flood persisted on the Earth before subsiding.

Manuscripts[edit]

In sports[edit]

In other fields[edit]

A Professor's Cube has 150 colored squares

150 is also:

The total number of dragon eggs in Spyro: Year of the Dragon.

See also[edit]

References[edit]

  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.