# 32 (number)

**32** (thirty-two; Roman numerals XXXII) is the natural number following 31 and preceding 33. It is the fifth power of two, \( 32 = 2^{5} \), a property that shapes both its arithmetic character and its prominence in computing, where it names a whole generation of processors, operating systems, and data formats.<sup>[1](https://oeis.org/wiki/32)</sup>

| Key fact | Detail |
|---|---|
| Prime factorization | \( 32 = 2^{5} \); its only prime factor is 2<sup>[2](https://mathworld.wolfram.com/PrimeFactor.html)</sup> |
| Divisors | Six divisors: 1, 2, 4, 8, 16, 32; the sum of proper divisors is 31, so 32 is a deficient number<sup>[3](https://numbermath.com/number/32)</sup> |
| Positional notations | Binary 100000, hexadecimal 20<sup>[4](https://www.numberpedia.app/number/32)</sup> |
| Chemistry | Atomic number of germanium (Ge), atomic weight 72.630<sup>[5](https://physics.nist.gov/PhysRefData/Handbook/Tables/germaniumtable1_a.htm)</sup> |
| Temperature | 32 °F is the freezing point of water at standard pressure on the Fahrenheit scale<sup>[6](https://www.weather.gov/ggw/GlossaryF)</sup> |
| Computing | The Intel 80386 (1985) was the first 32-bit processor in the IA-32 family, with a 32-bit address bus supporting up to 4 GB of physical memory<sup>[7](https://www.intel.com/content/dam/support/us/en/documents/processors/pentium4/sb/25366521.pdf)</sup> |
| Floating point | IEEE binary32 (single precision) stores a number in N = 32 bits with p = 24 significant bits<sup>[8](https://dlmf.nist.gov/3.1)</sup> |

## Arithmetic properties

Because 32 is a power of two, its divisors are exactly the smaller powers of two: 1, 2, 4, 8, 16, and 32, six in all.<sup>[3](https://numbermath.com/number/32)</sup> The sum of the proper divisors (all except 32 itself) is 31, one short of the number, which classifies 32 as a deficient number.<sup>[3](https://numbermath.com/number/32)</sup> As \( 2^{5} \), it is a perfect fifth power, the smallest nontrivial one after 1, since a fifth power requires every exponent in the prime factorization to be divisible by 5.<sup>[9](https://ayton.id.au/gary/Science/Ma_prime.htm)</sup>

In positional notation, 32 is written 100000 in binary, a one followed by five zeros, and 20 in hexadecimal.<sup>[4](https://www.numberpedia.app/number/32)</sup> The binary form follows directly from the power-of-two structure: \( 2^{5} \) occupies the sixth binary place. In the Collatz process (repeatedly halving even numbers and applying \( 3n+1 \) to odd ones), a starting value of 32 reaches 1 in five steps, again because it is a pure power of two.<sup>[3](https://numbermath.com/number/32)</sup>

The number 32 also appears as a count in divisor theory: OEIS sequence A175742 lists the integers with exactly 32 divisors, which have prime factorizations of the forms \( p^{31} \), \( p^{15}q \), \( p^{7}q^{3} \), \( p^{7}qr \), \( p^{3}q^{3}r \), \( p^{3}qrs \), and \( pqrst \) for distinct primes.<sup>[10](https://oeis.org/A175742)</sup>

## 32 in computing

**Word size and addressing.** A 32-bit integer can hold \( 2^{32} \) distinct values, and a 32-bit address can distinguish that many memory locations, about 4.29 billion. The [Intel 80386](https://www.edgepedia.org/intel-80386), introduced in October 1985, was the first 32-bit processor in the IA-32 architecture family: it introduced 32-bit registers for both operands and addressing, and its 32-bit address bus supported up to 4 GB of physical memory.<sup>[7](https://www.intel.com/content/dam/support/us/en/documents/processors/pentium4/sb/25366521.pdf)</sup> Intel spent $100 million developing the 386 and its support systems; in 1991, 386 sales alone accounted for about half of Intel's annual revenue.<sup>[11](https://timeline.intel.com/1985/raising-the-bar-with-the-386)</sup> The term "x86" became common after the 80386 and usually implies binary compatibility with its 32-bit instruction set.<sup>[12](https://community.intel.com/t5/Intel-Moderncode-for-Parallel/Architecture-in-Intel/m-p/1008281/highlight/true)</sup>

**Data formats.** The same word size fixed the shape of common data types. The [IEEE 754](https://www.edgepedia.org/ieee-754) binary32 format, formerly called single precision, stores a floating-point number in 32 bits with 24 significant bits, an exponent range from −126 to 127, and a machine precision of about \( 0.596 \times 10^{-7} \).<sup>[8](https://dlmf.nist.gov/3.1)</sup> [Internet Protocol](https://www.edgepedia.org/internet-protocol) version 4 (IPv4) uses 32-bit addresses, which is why the original internet address space contains about 4.29 billion locations.<sup>[13](https://numberwise.app/number/32)</sup> Integer division on many processors is implemented by multiplication with an approximation of the divisor's inverse, using unsigned 32-bit quantities with a 64-bit product, because this is usually much faster than a division instruction.<sup>[14](https://oeis.org/A346495)</sup>

**Decline of 32-bit platforms.** The 32-bit era is closing on the desktop. Valve announced that [Steam](https://www.edgepedia.org/steam-service) would stop supporting 32-bit versions of Windows as of January 1, 2026, citing that only 0.01% of Steam players still ran such systems and that 32-bit Windows was no longer compatible with drivers and libraries required for the client's core features.<sup>[15](https://www.tomshardware.com/video-games/pc-gaming/valve-to-drop-steam-support-for-32-bit-windows-versions-next-year-says-its-no-longer-compatible-with-core-client-features-only-0-01-percent-of-players-actually-used-it)</sup> A December 2025 client update made the Steam application itself fully 64-bit on Windows for the first time, while 32-bit Windows users stop receiving updates at the cutoff.<sup>[16](https://www.tomshardware.com/video-games/pc-gaming/steam-begins-64-bit-transition-on-windows-as-32-bit-support-enters-final-countdown)</sup> The distinction matters: many 32-bit applications continue to run under 64-bit operating systems through compatibility layers; what is ending is support for 32-bit operating systems themselves.<sup>[15](https://www.tomshardware.com/video-games/pc-gaming/valve-to-drop-steam-support-for-32-bit-windows-versions-next-year-says-its-no-longer-compatible-with-core-client-features-only-0-01-percent-of-players-actually-used-it)</sup>

## Science and everyday measure

The element with atomic number 32 is germanium, a silvery-white metalloid once widely used in transistors and now used mainly in infrared optics and wide-angle lenses; its standard atomic weight is 72.630.<sup>[5](https://physics.nist.gov/PhysRefData/Handbook/Tables/germaniumtable1_a.htm)</sup><sup> • </sup><sup>[17](https://periodic-table.rsc.org/element/32/germanium)</sup>

On the [Fahrenheit](https://www.edgepedia.org/fahrenheit) scale, water freezes at 32 °F and boils at 212 °F, and the conversion from Celsius uses the number directly: \( \degree F = (\degree C \times 9/5) + 32 \).<sup>[6](https://www.weather.gov/ggw/GlossaryF)</sup> Daniel Fahrenheit originally set 0 degrees at the freezing point of a salt-water solution and 96 at human body temperature; the fixed points were later changed so the freezing point of water sat at 32 degrees and its boiling point at 212, values easier to reproduce in different laboratories.<sup>[18](https://www.nist.gov/si-redefinition/kelvin/kelvin-history)</sup>

## References

1. [32, OeisWiki](https://oeis.org/wiki/32)
2. [Prime Factor, Wolfram MathWorld](https://mathworld.wolfram.com/PrimeFactor.html)
3. [Number 32 (thirty-two), Math.Number](https://numbermath.com/number/32)
4. [Number 32: Properties, Factors & Math Facts, NumberPedia](https://www.numberpedia.app/number/32)
5. [Atomic Data for Germanium (Ge), NIST](https://physics.nist.gov/PhysRefData/Handbook/Tables/germaniumtable1_a.htm)
6. [National Weather Service Glossary: Fahrenheit](https://www.weather.gov/ggw/GlossaryF)
7. [Intel 64 and IA-32 Architectures Software Developer's Manual](https://www.intel.com/content/dam/support/us/en/documents/processors/pentium4/sb/25366521.pdf)
8. [DLMF §3.1: Arithmetics and Error Measures, NIST](https://dlmf.nist.gov/3.1)
9. [Special Numbers (perfect powers reference)](https://ayton.id.au/gary/Science/Ma_prime.htm)
10. [A175742: Numbers with 32 divisors, OEIS](https://oeis.org/A175742)
11. [Raising the Bar with the 386, Intel Timeline](https://timeline.intel.com/1985/raising-the-bar-with-the-386)
12. [Architecture in Intel, Intel Community](https://community.intel.com/t5/Intel-Moderncode-for-Parallel/Architecture-in-Intel/m-p/1008281/highlight/true)
13. [32, Meaning, History and Connections, Numberwise](https://numberwise.app/number/32)
14. [A346495, OEIS (division by multiplication with 32-bit quantities)](https://oeis.org/A346495)
15. [Valve to drop Steam support for 32-bit Windows versions, Tom's Hardware](https://www.tomshardware.com/video-games/pc-gaming/valve-to-drop-steam-support-for-32-bit-windows-versions-next-year-says-its-no-longer-compatible-with-core-client-features-only-0-01-percent-of-players-actually-used-it)
16. [Steam begins 64-bit transition on Windows as 32-bit support enters final countdown, Tom's Hardware](https://www.tomshardware.com/video-games/pc-gaming/steam-begins-64-bit-transition-on-windows-as-32-bit-support-enters-final-countdown)
17. [Germanium, Royal Society of Chemistry Periodic Table](https://periodic-table.rsc.org/element/32/germanium)
18. [Kelvin: History, NIST](https://www.nist.gov/si-redefinition/kelvin/kelvin-history)

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*Topic: Encyclopedia › Physical world and mathematics › Mathematics and statistics › Numbers and algebra › Arithmetic and number systems › Integer sequences and partitions › Special and named integers › Powers and perfect powers*

*Initially written Sep 17, 2026 · Reviewed: Sep 30, 2026; Oct 15, 2026 · Edited: Sep 30, 2026; Oct 15, 2026 · Last review: Oct 15, 2026*

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License: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license