| ||||
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Cardinal | thirty-three | |||
Ordinal | 33rd (thirty-third) | |||
Factorization | 3 × 11 | |||
Divisors | 1, 3, 11, 33 | |||
Greek numeral | ΛΓ´ | |||
Roman numeral | XXXIII | |||
Binary | 1000012 | |||
Ternary | 10203 | |||
Senary | 536 | |||
Octal | 418 | |||
Duodecimal | 2912 | |||
Hexadecimal | 2116 |
33 (thirty-three) is the natural number following 32 and preceding 34.
33 is the 21st composite number, and 8th distinct semiprime (third of the form where is a higher prime). [1] It is one of two numbers to have an aliquot sum of 15 = 3 × 5 — the other being the square of 4 — and part of the aliquot sequence of 9 = 32 in the aliquot tree (33, 15, 9, 4, 3, 2, 1).
It is the largest positive integer that cannot be expressed as a sum of different triangular numbers, and it is the largest of twelve integers that are not the sum of five non-zero squares; [2] on the other hand, the 33rd triangular number 561 is the first Carmichael number. [3] [4] 33 is also the first non-trivial dodecagonal number (like 369, and 561) [5] and the first non-unitary centered dodecahedral number. [6]
It is also the sum of the first four positive factorials, [7] and the sum of the sum of the divisors of the first six positive integers; respectively: [8]
It is the first member of the first cluster of three semiprimes 33, 34, 35; the next such cluster is 85, 86, 87. [9] It is also the smallest integer such that it and the next two integers all have the same number of divisors (four). [10]
33 is the number of unlabeled planar simple graphs with five nodes. [11]
33 is equal to the sum of the squares of the digits of its own square in nonary (14409), hexadecimal (44116) and unotrigesimal (14431). For numbers greater than 1, this is a rare property to have in more than one base. It is also a palindrome in both decimal and binary (100001).
33 was the second to last number less than 100 whose representation as a sum of three cubes was found (in 2019): [12]
Importantly, the ratio of prime numbers to non-primes at 33 in the sequence of natural numbers (up to) is , where there are (inclusively) 11 prime numbers and 22 non-primes (i.e., when including 1).
Where 33 is divisible by the number of prime numbers below it (11), the product is the seventh numerator of harmonic number , [13] where specifically, the previous such numerators are 49 and 137, which are respectively the thirty-third composite and prime numbers. [14] [15]
A positive definite quadratic integer matrix represents all odd numbers when it contains at least the set of seven integers: [16] [17]
Thirty-three is:
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.
12 (twelve) is the natural number following 11 and preceding 13. Twelve is a superior highly composite number, divisible by the numbers 2, 3, 4, and 6.
15 (fifteen) is the natural number following 14 and preceding 16.
21 (twenty-one) is the natural number following 20 and preceding 22.
90 (ninety) is the natural number following 89 and preceding 91.
28 (twenty-eight) is the natural number following 27 and preceding 29.
27 is the natural number following 26 and preceding 28.
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.
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.
300 is the natural number following 299 and preceding 301.
360 is the natural number following 359 and preceding 361.
144 is the natural number following 143 and preceding 145.
135 is the natural number following 134 and preceding 136.
138 is the natural number following 137 and preceding 139.
168 is the natural number following 167 and preceding 169.
177 is the natural number following 176 and preceding 178.
20,000 is the natural number that comes after 19,999 and before 20,001.
888 is the natural number following 887 and preceding 889.