# 33 (number)

 ← 32 33 34 →
Cardinalthirty-three
Ordinal33rd
(thirty-third)
Factorization3 × 11
Divisors1, 3, 11, 33
Greek numeralΛΓ´
Roman numeralXXXIII
Binary1000012
Ternary10203
Quaternary2014
Quinary1135
Senary536
Octal418
Duodecimal2912
Vigesimal1D20
Base 36X36

33 (thirty-three) is the natural number following 32 and preceding 34.

## In mathematics

33 is:

• the largest positive integer that cannot be expressed as a sum of different triangular numbers.
• the smallest odd repdigit that is not a prime number.
• the sum of the first four positive factorials.
• the sum of the sum of the divisors of the first 6 positive integers.
• the sum of three cubes: ${\displaystyle 33=8866128975287528^{3}+(-8778405442862239)^{3}+(-2736111468807040)^{3}.}$.[1]
• equal to the sum of the squares of the digits of its own square in bases 9, 16 and 31.
For numbers greater than 1, this is a rare property to have in more than 1 base.
• the smallest integer such that it and the next two integers all have the same number of divisors.
• the first member of the first cluster of three semiprimes (33, 34, 35); the next such cluster is 85, 86, 87.

## In science

• The atomic number of arsenic
• A normal human spine has 33 vertebrae when the bones that form the coccyx are counted individually
• 33 is, according to the Newton scale, the temperature at which water boils.

## In other fields

Thirty-three is:

• A significant number in modern numerology, one of the master numbers along with 11 and 22.
• The number printed on all Rolling Rock beer labels.
• Pabst Blue Ribbon Beer used to be advertised as "Blended 33 to 1".
• The namesake of the private club, Club 33, located in Disneyland's New Orleans Square.
• The number of workers trapped, all of whom were rescued, during the 2010 Copiapó mining accident.
• One of the symbols of Ku Klux Klan. (K is the 11th letter of the alphabet; 3 times 11 is 33, KKK).
• The 33 Orientales were a group of Uruguay's national Independence Heroes that liberate the country in 1825 from the Brazilian Empire, the name is due for the leaders all 33 Degree Masons (The Thirty-Three Orientals), one of Uruguay's national states and its capital city is named "Treinta y Tres" after them
• +33 is the code for international direct-dial phone calls to France.

## References

1. ^ Booker, Andrew R. (2019). "Cracking the problem with 33" (pdf). University of Bristol. arXiv:1903.04284.
2. ^ Insights #517, October 8, 2010.
3. ^ de Vries, Ad (1976). Dictionary of Symbols and Imagery. Amsterdam: North-Holland Publishing Company. p. 462. ISBN 978-0-7204-8021-4.
4. ^ Ghazzālī; Karim, Fazlul. "Imam Gazzali's Ihya Ulum-id-din: pt. 1 and 2. The book of constructive virtues". Sind Sagar Academy. Retrieved 21 March 2018 – via Google Books.