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Cardinal | one hundred forty-four | |||
Ordinal | 144th (one hundred forty-fourth) | |||
Factorization | 24 × 32 | |||
Divisors | 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 | |||
Greek numeral | ΡΜΔ´ | |||
Roman numeral | CXLIV | |||
Binary | 100100002 | |||
Ternary | 121003 | |||
Senary | 4006 | |||
Octal | 2208 | |||
Duodecimal | 10012 | |||
Hexadecimal | 9016 |
144 (one hundred [and] forty-four) is the natural number following 143 and preceding 145.
It represents a dozen dozens, or one gross . It is the number of square inches in a square foot.
In number theory, 144 is the twelfth Fibonacci number; it is the only Fibonacci number (other than 0, and 1) to also be a square. [1] [2]
144 is the square of 12. It is also the twelfth Fibonacci number, following 89 and preceding 233, and the only Fibonacci number (other than 0, and 1) to also be a square. [3] [4] 144 is the smallest number with exactly 15 divisors, but it is not highly composite since the smaller number 120 has 16 divisors. [5] 144 is also equal to the sum of the eighth twin prime pair, (71 + 73). [6] [7] It is divisible by the value of its φ function, which returns 48 in its case, [8] and there are 21 solutions to the equation This is more than any integer below it, which makes it a highly totient number. [9] In decimal, 144 is the largest of only four sum-product numbers, [10] and it is a Harshad number, where , which divides 144. [11]
144 is 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. It was famously published in a paper by both authors, whose body consisted of only two sentences: [12]
A direct search on the CDC 6600 yielded
275 + 845 + 105 + 1335 = 1445
as the smallest instance in which four fifth powers sum to a fifth power. This is a counterexample to a conjecture by Euler that at least nnth powers are required to sum to an nth power, n > 2.
In decimal notation, when each of the digits in the expression of the square of twelve are reversed, the equation remains true:
Another number that shares this property is 169, where , while
A regular ten-sided decagon has an internal angle of 144 degrees, which is equal to four times its own central angle, and equivalently twice the central angle of a regular five-sided pentagon, while in four dimensions, the snub 24-cell, one of three semiregular polytopes in the fourth dimension, contains a total of 144 polyhedral cells: 120 regular tetrahedra and 24 regular icosahedra. Meanwhile, the maximum determinant in a 9 by 9 matrix of zeroes and ones is 144. [13]
144 is the sum of the divisors of 70: , [14] where 70 is part of the only solution to the cannonball problem aside from the trivial solution, in-which the sum of the squares of the first twenty-four integers is equal to the square of another integer, 70 — and meaningful in the context of constructing the Leech lattice in twenty-four dimensions via the Lorentzian even unimodular lattice II25,1. [15] : pp.2–11 [16] 144 is relevant in testing whether two vectors in the quaternionic Leech lattice are equivalent under its automorphism group, Conway group : modulo , every vector is congruent to either or a minimal vector that is one of algebraic coordinate-frames, in-which a frame sought can be carried to its standard frame that is then checked for equivalence under a group stabilizing the frame of interest. [17] [18] [19]
10 (ten) is the even natural number following 9 and preceding 11. Ten is the base of the decimal numeral system, the most common system of denoting numbers in both spoken and written language.
111 is the natural number following 110 and preceding 112.
90 (ninety) is the natural number following 89 and preceding 91.
24 (twenty-four) is the natural number following 23 and preceding 25. It is one sixth of a gross or two dozen.
72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or 6 dozen.
34 (thirty-four) is the natural number following 33 and preceding 35.
104 is the natural number following 103 and preceding 105.
100 or one hundred is the natural number following 99 and preceding 101.
1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.
360 is the natural number following 359 and preceding 361.
180 is the natural number following 179 and preceding 181.
700 is the natural number following 699 and preceding 701.
600 is the natural number following 599 and preceding 601.
800 is the natural number following 799 and preceding 801.
2000 is a natural number following 1999 and preceding 2001.
4000 is the natural number following 3999 and preceding 4001. It is a decagonal number.
135 is the natural number following 134 and preceding 136.
168 is the natural number following 167 and preceding 169.
744 is the natural number following 743 and preceding 745.
888 is the natural number following 887 and preceding 889.