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 ${\displaystyle 3\times q}$ where ${\displaystyle q}$ is a higher prime). 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; on the other hand, the 33rd triangular number 561 is the first Carmichael number. 33 is also the first non-trivial dodecagonal number (like 369, and 561) and the first non-unitary centered dodecahedral number.

It is also the sum of the first four positive factorials, and the sum of the sums of the divisors of the first six positive integers; respectively: $${\displaystyle {\begin{aligned}33&=1!+2!+3!+4!=1+2+6+24\\33&=1+3+4+7+6+12\\\end{aligned}}}$$

It is the first member of the first cluster of three semiprimes 33, 34, 35; the next such cluster is 85, 86, 87. It is also the smallest integer such that it and the next two integers all have the same number of divisors (four).

33 is the number of unlabeled planar simple graphs with five nodes.

There are only five regular polygons that are used to tile the plane uniformly (the triangle, square, hexagon, octagon, and dodecagon); the total number of sides in these is: 3 + 4 + 6 + 8 + 12 = 33.

33 is equal to the sum of the squares of the digits of its own square in nonary (1440₉), hexadecimal (441₁₆) and untrigesimal (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).