Regular number
numbers that evenly divide powers of 60
Regular numbers are numbers that evenly divide powers of 60 (or, equivalently, powers of 30). Equivalently, they are the numbers whose only prime divisors are 2, 3, and 5. As an example, 602 = 3600 = 48 × 75, so as divisors of a power of 60 both 48 and 75 are regular.
These numbers arise in several areas of mathematics and its applications, and have different names coming from their different areas of study.
In number theory, these numbers are called 5-smooth, because they can be characterized as having only 2, 3, or 5 as their prime factors. This is a specific case of the more general k-smooth numbers, the numbers that have no prime factor greater than k.
In the study of Babylonian mathematics, the divisors of powers of 60 are called regular numbers or regular sexagesimal numbers, and are of great importance in this area because of the sexagesimal (base 60) number system that the Babylonians used for writing their numbers, and that was central to Babylonian mathematics.
In music theory, regular numbers occur in the ratios of tones in five-limit just intonation. In connection with music theory and related theories of architecture, these numbers have been called the harmonic whole numbers.
In computer science, regular numbers are often called Hamming numbers, after Richard Hamming, who proposed the problem of finding computer algorithms for generating these numbers in ascending order.
This brief starts where responsible research should: with the source description of “Regular number” as numbers that evenly divide powers of 60. Everything that follows is an evidence route, not borrowed authority.
Why this record matters
The subject matters to the general reference register because the source frames it as numbers that evenly divide powers of 60. Its deeper value depends on whether names, dates, institutions and citations support that framing.
Vocabulary and entity names are the principal evidence signals here, because they determine the precision of every later search. The source revision retrieved here is dated Sep 16, 2026. The linked authority identifier is Q1826416. None of the 0 selected statements returned an explicit reference.
Overview language is designed for orientation and should not be treated as a substitute for the evidence cited beneath it. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “Regular number”, its source revision and the description used here.
- Expand the search: follow Regular number primary sources, Regular number archive and Regular research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “Regular number”?
- What terminology or title could unlock a more precise catalogue search?
- Which cited source is closest to the event, object or claim?
Search terms from this dossier
This entry incorporates text from “Regular number” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.