144 (number)

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← 143 144 145 →
Cardinalone hundred forty-four
Ordinal144th
(one hundred forty-fourth)
Factorization24× 32
Divisors1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Greek numeralΡΜΔ´
Roman numeralCXLIV
Binary100100002
Ternary121003
Quaternary21004
Quinary10345
Senary4006
Octal2208
Duodecimal10012
Hexadecimal9016
Vigesimal7420
Base 364036

144 (one hundred [and] forty-four) is the natural number following 143 and preceding 145. 144 is a dozen dozens, or one gross.

In mathematics[edit]

144 is the twelfth Fibonacci number, and the largest one to also be a square,[1] as the square of 12 (which is also its index in the Fibonacci sequence), following 89 and preceding 233.

144 is the smallest number with exactly 15 divisors, but it is not highly composite since a smaller number 120 has 16 divisors.

144 is divisible by the value of its φ function, which returns 48 in this case. Also, there are 21 solutions to the equation φ(x) = 144, more than any integer below 144, making it a highly totient number.[2]

1445 = 275 + 845 + 1105 + 1335, the smallest number whose fifth power is a sum of four (smaller) fifth powers. This solution was found in 1966 by L. J. Lander and T. R. Parkin, and disproved Euler's sum of powers conjecture.

The maximum determinant in a 9 by 9 matrix of zeroes and ones is 144.

144 is in base 10 a sum-product number, as well as a Harshad number.[3] 144 is a repdigit in bases 15, 17, 23, 35, 47, 71, and 143. 144 is the sum of a twin prime pair (71 + 73)

In the military[edit]

In sports[edit]

In transportation[edit]

In other fields[edit]

144 is also:

See also[edit]

References[edit]

  1. ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 165
  2. ^ "Sloane's A097942 : Highly totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  3. ^ "Sloane's A005349 : Niven (or Harshad) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  4. ^ College Hoops Net
  5. ^ Porter, Darwin; Danforth Prince (2009). Frommer's Austria. Hoboken, New Jersey: Frommer's. p. 482. ISBN 978-0-470-39897-5.
  6. ^ Erste Hilfe - Notfall Nummern

External links[edit]