144 (number)
Encyclopedia : 1 : 14 : 144 : 144 (number)
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| Cardinal | One hundred [and] forty four |
| Ordinal | 144th |
| Factorization | [ 2^4 \cdot 3^2 ] |
| Divisors | 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 |
| Roman numeral | CXLIV |
| Binary | 10010000 |
| Octal | 220 |
| Duodecimal | 100 |
| Hexadecimal | 90 |
In mathematics
It is the twelfth Fibonacci number, and the largest one to also be a square, as the square of 12 (which is also its index in the Fibonacci sequence), following 121 and preceding 169.144 is the smallest number with exactly 15 divisors.
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.
[144^5 = 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.
The maximum determinant in an 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 and a Zuckerman number.
In other fields
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).
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