144 (Number)

CardinalOne hundred and
forty four
Ordinal144th
Factorization 2^4 \cdot 3^2
Roman numeralCXLIV
Binary10010000
Hexadecimal90
144 is the natural number following 143 and preceding 145. 144 is a dozen dozens, or one gross. It is the twelfth Fibonacci number, and the largest one to also be a square. It is a Harshad number. 144 is a number that 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. 144 is the 12th square number, following 121 and preceding 169. 144^5 = 27^5 + 84^5 + 110^5 + 133^5, the smallest number whose fifth power is a sum of less than five (smaller) fifth powers. This solution was found in 1967 by L.J. Lander and T.R. Parkin, and disproved a conjecture by Euler. 144 is also:
  • The measurement, in cubits, of the wall of New Jerusalem shown by the seventh angel (Holy Bible, Revelation 21:17).
  • The Intel 8086 instruction for no operation (NOP).
For the year AD 144, see 144.

 

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