# 32 (number)

 ← 31 32 33 →
Cardinal thirty-two
Ordinal 32nd
(thirty-second)
Factorization 25
Divisors 1, 2, 4, 8, 16, 32
Roman numeral XXXII
Binary 1000002
Ternary 10123
Quaternary 2004
Quinary 1125
Senary 526
Octal 408
Duodecimal 2812
Vigesimal 1C20
Base 36 W36

32 (thirty-two) is the natural number following 31 and preceding 33.

## In mathematics

32 is the smallest number n with exactly 7 solutions to the equation φ(x) = n. It is also the sum of the totient function for the first ten integers.

The fifth patower of two, 32 is also a Leyland number since 24 + 42 = 32.

As with every power of two, 32 has an aliquot sum one less than itself: the prime 31. 32 is the first member of the 31-aliquot tree.

32 is the ninth happy number.

32 = 11 + 22 + 33

## In science

• The freezing point of water at sea level in degrees Fahrenheit

### Astronomy

• The Saros number of the solar eclipse series which began on September 24, 1957 BC and ended on March 10, 460 BC. The duration of Saros series 32 was 1496.5 years, and it contained 84 solar eclipses.
• The Saros number of the lunar eclipse series which began on June 11, 1691 BC and ended on August 9, 375 BC. The duration of Saros series 32 was 1316.2 years, and it contained 74 lunar eclipses.

## In religion

In the Kabbalah, there are 32 Kabbalistic Paths of Wisdom.

One of the central texts of the Pāli Canon in the Theravada Buddhist tradition, the Digha Nikaya, describes the appearance of the historical Buddha with a list of 32 physical characteristics.

The Hindu scripture Mudgala Purana also describes Ganesha as taking 32 forms.

## In sports

In chess, the total number of black squares on the board, the total number of white squares, and the total number of pieces (black and white) at the beginning of the game.

The jersey number 32 has been retired by several North American sports teams in honor of past playing greats:

The number of teams in the National Football League.

The number of national teams that have participated in each FIFA World Cup finals tournament since 1998.

The ball used in association football is typically made with 32 panels of leather or synthetic material.

## In other fields

Thirty-two could also refer to: