33 (number)

33
Cardinal thirty-three
Ordinal 33rd
(thirty-third the number 33)
Factorization 3 \cdot 11
Divisors 1, 3, 11, 33
Roman numeral XXXIII
Binary 1000012
Octal 418
Duodecimal 2912
Hexadecimal 2116

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

Contents

In mathematics

33 is the largest positive integer that cannot be expressed as a sum of different triangular numbers. It is also the smallest odd repdigit that is not a prime number.

33 is the eighth distinct semiprime comprising the prime factors (3 • 11). Its aliquot sum is 15; itself a discrete semiprime (3 • 5) in the following Aliquot sequence 33,15,9,4,3,1,0. (Note 33 is the 8th composite number to descend into the prime number 3, the others outside of this sequence being 30,26,16,12) Since 33 is a semiprime with both its prime factors being Gaussian primes, 33 is a Blum integer.

The sum of the first four positive factorials is 33. Adding up the sums of divisors of 1 through 6 yields 33. 33 is the smallest integer such that it and the next two integers all have the same number of divisors.

It is also the first member of the first cluster of three semiprimes (33,34,35); the next such cluster is 85,86,87.

Since the greatest prime factor of 332 + 1 = 1090 is 109, which is obviously more than 33 twice, 33 is a Størmer number.

In science

Astronomy

In religion

In sports

The number of innings played in the longest baseball game in history (a 1981 minor league game between the Rochester Red Wings and the Pawtucket Red Sox in Pawtucket, Rhode Island).

The jersey number 33 has been retired by several North American sports teams in honor of past playing greats:

In motorsport, 33 is:

The Big 33 Football Classic is an annual postseason high school football all-star game that features top players from Pennsylvania. In recent years, the opposition has been an all-star team from Ohio. The number 33 represents the original number of players on each squad (now 34).

FIBA 33 is a formalized version of half-court three-on-three basketball currently being heavily promoted by the sport's international governing body, FIBA. In this variant, the game ends by rule once either team has scored at least 33 points, with scoring following traditional basketball rules.

In other fields

Thirty-three is:

Historical years

33 A.D., 33 B.C., 1933

References

  1. ^ Insights #517, October 8, 2010.
  2. ^ de Vries, Ad (1976). Dictionary of Symbols and Imagery. Amsterdam: North-Holland Publishing Company. pp. 462. ISBN 0-7204-8021-3. 
  3. ^ Imam Gazzali's Ihya ulum-id-din, Volume 4