# 10,000,000,000

**10,000,000,000** (ten billion, or \( 10^{10} \)) is the natural number equal to ten thousand million, written as a 1 followed by ten zeros. In the short scale used in [American English](https://www.edgepedia.org/american-english) and, since 1974, in official British usage, it is ten billion; in the historical long scale it would be described as ten thousand million, since the long-scale word "billion" meant \( 10^{12} \).<sup>[1](https://commonslibrary.parliament.uk/research-briefings/sn04440/)</sup>

| Key fact | Detail |
|---|---|
| Value and name | Ten billion (short scale); \( 10^{10} \), a 1 followed by ten zeros<sup>[2](https://metanumbers.com/10000000000)</sup> |
| Prime factorization | \( 2^{10} \times 5^{10} \), with 2 distinct and 20 total prime factors<sup>[2](https://metanumbers.com/10000000000)</sup> |
| Divisors | 121 positive divisors, of which 110 are even and 11 are odd; their sum is 24,987,792,457<sup>[2](https://metanumbers.com/10000000000)</sup> |
| Euler totient | \( \varphi(n) = 4{,}000{,}000{,}000 \), the count of integers from 1 to n that are coprime to n<sup>[2](https://metanumbers.com/10000000000)</sup> |
| As a duration | \( 10^{10} \) seconds is about 316.89 years, roughly 317 years<sup>[3](https://www.calculateme.com/time/seconds/to-years/10000000000)</sup> |
| Population milestone | World population is projected to reach 10 billion in 2059 and peak at 10.6 billion in 2092 (US Census Bureau projections)<sup>[4](https://www.census.gov/data/data-tools/population-clock/world-notes.html)</sup> |
| SI position | No single SI prefix exists for \( 10^{10} \); it lies between giga (\( 10^{9} \)) and tera (\( 10^{12} \))<sup>[5](https://www.nist.gov/pml/special-publication-330/sp-330-section-3)</sup> |

## Arithmetic properties

Because ten billion is a power of ten, its prime factorization is simple: \( 10^{10} = (2 \cdot 5)^{10} = 2^{10} \times 5^{10} \). It is a composite number with exactly two distinct prime factors, 2 and 5, and twenty prime factors counted with multiplicity.<sup>[2](https://metanumbers.com/10000000000)</sup> The divisor count follows from the exponents: for a number \( p^{a} \cdot q^{b} \) the number of divisors is \( (a+1)(b+1) \), so here \( 11 \cdot 11 = 121 \).<sup>[2](https://metanumbers.com/10000000000)</sup>

The divisor structure gives several derived quantities. The 121 divisors sum to 24,987,792,457, their geometric mean is 100,000 (which equals \( \sqrt{n} \), as it does for any square), and the Euler totient is \( 4 \times 10^{9} \), since a random integer is coprime to \( 10^{10} \) exactly when it is divisible by neither 2 nor 5.<sup>[2](https://metanumbers.com/10000000000)</sup> The number can be written as a sum of two squares in 44 ways, and the count of primes up to ten billion is approximately 454,721,050.<sup>[2](https://metanumbers.com/10000000000)</sup>

## Naming and the long and short scales

**Two scales, one word.** English names for large numbers follow one of two systems. In the short scale, each new term after million is a thousand times the previous one, so a billion is a thousand million (\( 10^{9} \)) and ten billion is \( 10^{10} \). In the long scale, each new term is a million times the previous one, so billion meant a million millions (\( 10^{12} \)), and \( 10^{10} \) has no single-word name, being expressed as ten thousand million.<sup>[1](https://commonslibrary.parliament.uk/research-briefings/sn04440/)</sup>

The word "billion" first appears with the long-scale value \( 10^{12} \) in French in 1484, in *Le Triparty en la Science des Nombres* by Nicolas Chuquet (1445?–1500?).<sup>[6](https://mathshistory.st-andrews.ac.uk/Miller/mathword/m/)</sup> Before the 20th century there was no uniformity: the word meant a thousand million (\( 10^{9} \)) in the United States and a million million (\( 10^{12} \)) in England, while France commonly used "milliard" for \( 10^{9} \).<sup>[6](https://mathshistory.st-andrews.ac.uk/Miller/mathword/m/)</sup> In 1974 the British Prime Minister Harold Wilson confirmed in a written parliamentary reply that British ministers would use "billion" to mean a thousand million, in conformity with international usage, and official UK statistics now use the short scale.<sup>[1](https://commonslibrary.parliament.uk/research-briefings/sn04440/)</sup> Because of the residual ambiguity, United Nations statistical publications avoid the word entirely, writing "thousand million" for \( 10^{9} \) and "million million" for \( 10^{12} \).<sup>[7](https://unstats.un.org/unsd/energy/meetings/2013ees/2013ktce.pdf)</sup>

In the [International System of Units](https://www.edgepedia.org/international-system-of-units), \( 10^{10} \) falls in the gap between the prefixes giga (\( 10^{9} \), symbol G) and tera (\( 10^{12} \), symbol T); SI provides no prefix for \( 10^{10} \) itself, so quantities of this size are written as ten gigawatts, ten gigabytes, and so on, or in scientific notation.<sup>[5](https://www.nist.gov/pml/special-publication-330/sp-330-section-3)</sup> Style guides recommend writing the word out, as "10 billion", rather than abbreviating it.<sup>[8](https://www.bristol.gov.uk/bristol-style/a-to-z-of-style/a-to-z-of-style-item?id=59)</sup>

## Ten billion as a quantity

**Time.** A common way to grasp the size of \( 10^{10} \) is through seconds: ten billion seconds is about 316.89 years, so a span of ten billion seconds reaches back to the late seventeenth or early eighteenth century.<sup>[3](https://www.calculateme.com/time/seconds/to-years/10000000000)</sup> [Reference](https://www.edgepedia.org/reference) tables of natural timescales place \( 10^{10} \) seconds at 317 years, one step above one billion seconds (31.7 years) and one step below one hundred billion seconds (3,171 years).<sup>[9](https://virtualmmx.ddns.net/gbooks/TimeInPowersOfTenNaturalPhenomenaAndTheirTimescales.pdf)</sup>

**Population.** Ten billion is also a projected milestone for the human population. According to estimates and projections in the vintage 2025 release of the US Census Bureau's International Database, the world population reached 7 billion in 2011 and 8 billion in 2023, is projected to reach 9 billion in 2038 and 10 billion in 2059, and to peak at 10.6 billion in 2092 before declining.<sup>[4](https://www.census.gov/data/data-tools/population-clock/world-notes.html)</sup> The United Nations World Population Prospects 2024 revision gives a somewhat lower and earlier peak, around 10.3 billion people in the mid-2080s, up from 8.2 billion in 2024.<sup>[10](https://desapublications.un.org/file/20847/download)</sup> The two projections differ in peak size and timing, a normal consequence of different fertility and mortality assumptions, and both are regularly revised as new data arrive.<sup>[4](https://www.census.gov/data/data-tools/population-clock/world-notes.html)</sup>

**Astronomy.** The quantity also appears as a mass scale for the largest known black holes: observations reported central black holes of 9.7 billion solar masses in NGC 3842 and a comparable or greater mass in NGC 4889, the first black holes reliably measured at around ten billion solar masses.<sup>[11](https://arxiv.org/abs/1112.1078)</sup>

## References

1. [What is a billion? And other large numbers, House of Commons Library](https://commonslibrary.parliament.uk/research-briefings/sn04440/)
2. [10000000000 (Number), Metanumbers](https://metanumbers.com/10000000000)
3. [Convert 10,000,000,000 Seconds to Years, CalculateMe](https://www.calculateme.com/time/seconds/to-years/10000000000)
4. [Notes on the World Population Clock, US Census Bureau](https://www.census.gov/data/data-tools/population-clock/world-notes.html)
5. [SP 330, Section 3: Decimal multiples and sub-multiples of SI units, NIST](https://www.nist.gov/pml/special-publication-330/sp-330-section-3)
6. [Earliest Known Uses of Some of the Words of Mathematics (M), MacTutor History of Mathematics](https://mathshistory.st-andrews.ac.uk/Miller/mathword/m/)
7. [Technical Notes, UN Statistics Division](https://unstats.un.org/unsd/energy/meetings/2013ees/2013ktce.pdf)
8. [A to Z of style: Numbers, Bristol City Council](https://www.bristol.gov.uk/bristol-style/a-to-z-of-style/a-to-z-of-style-item?id=59)
9. [Time in Powers of Ten: Natural Phenomena and Their Timescales](https://virtualmmx.ddns.net/gbooks/TimeInPowersOfTenNaturalPhenomenaAndTheirTimescales.pdf)
10. [World Population Prospects 2024: Summary of Results, United Nations](https://desapublications.un.org/file/20847/download)
11. [Two ten-billion-solar-mass black holes at the centres of giant elliptical galaxies, arXiv](https://arxiv.org/abs/1112.1078)

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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 › Named large numbers and number naming systems*

*Initially written Sep 17, 2026 · Reviewed: Sep 20, 2026; Sep 30, 2026; Oct 15, 2026 · Edited: Sep 30, 2026; Oct 15, 2026 · Last review: Oct 15, 2026*

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