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Research draft

divisor

vr.tr.divisor · XCT.QTY

Let an agent handle divisors by definition, computation, properties and applications in number theory.

Thing Registry Cross-cutting context

Research draft, second pass

A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.

written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify

Researched by: Claude

Purpose and description

Let an agent handle divisors by definition, computation, properties and applications in number theory.

An integer that divides another integer without remainder; for example the divisors of 12 are 1, 2, 3, 4, 6 and 12, with proper, common and trivial divisors as related notions.

What it is for: Factoring, simplifying fractions and number theory.

It can be list divisors of a number; find greatest common divisors; count and sum divisors; test divisibility.

Distinguishing features

Divides without remainder

Every integer has trivial divisors

Linked to prime factorisation

Used in GCD and fractions

What it looks like

Numbers dividing others exactly.

How it is recognised

Notation a | b

Divisor lists

Divisor in division (the number divided by) is a related sense

Related models

is a kind of - category

integer and factor

is related to - factorisation

prime number

is used in - application

fraction simplification

is studied in - field

number theory

In practice

Families and kinds

proper divisors

common divisors

greatest common divisor

prime divisors

divisor functions

Standards and regulation

ISO 80000-2 notation

Failure modes and hazards

Forgetting negative or trivial divisors

Confusing divisor and dividend

Also called

proper divisorcommon divisornon-trivial divisortrivial divisor

Where this came from

wikidata · CC0 1.0

Source repository Registry entry point

Also registered as vr.tr.divisor

Drafted structure

Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.

Computation Finding divisors.

Methods help.

List

All divisors.

List

Divisors.

  1. What are all the divisors of this number? measurement
  2. How is prime factorisation used? action

GCD

Common divisors.

GCD

Greatest common divisor.

  1. What is the greatest common divisor? measurement
  2. Which algorithm computes it? definition
Properties Theory.

Properties enable proofs.

Count

Number of divisors.

Count

Divisor count.

  1. How many divisors does it have? measurement
  2. What is their sum? measurement

Special numbers

Perfect and abundant.

Special

Special numbers.

  1. Is the number perfect, abundant or deficient? definition
  2. How is that determined? definition
Divisibility Tests.

Tests speed up checks.

Rules

Divisibility rules.

Rules

Divisibility rules.

  1. Which divisibility rule applies? definition
  2. Does the number pass? boundary

Fractions

Simplifying.

Fractions

Simplifying fractions.

  1. How can the fraction be simplified? action
  2. Is it in lowest terms? boundary
Learning Teaching.

Clear language helps.

Terms

Divisor and dividend.

Terms

Terminology.

  1. Which number is the divisor and which the dividend? definition
  2. How are factor and divisor related? definition

Computing

Algorithms.

Computing

Computing.

  1. How are divisors computed efficiently? action
  2. How large can inputs be? measurement

What the second pass must settle

  • Should divisor functions be separate entries?
  • How should OEIS sequences be linked?
  • How should the division sense be clarified?
Draft as JSON