Divisibility is one of the most important properties of integers which is fundamental to number theory. We start with some basic definitions.

| | | | created: 2014-02-20 21:37:44 | modified: 2019-03-09 17:21:54 | by: *bookofproofs*

## 1.**Definition**: Divisor, Complementary Divisor, Multiple

## 2.**Proposition**: Sign of Divisors of Integers

## 3.**Proposition**: Finite Number of Divisors

## 4.**Definition**: Divisor-Closed Sets

## 5.**Proposition**: Divisibility Laws

## 6.**Definition**: Sets of Integers Co-Prime To a Given Integer

## 7.**Definition**: Even and Odd Numbers

## 8.**Lemma**: Division with Quotient and Remainder (Euclid)

## 9.**Proposition**: Least Common Multiple

## 10.**Proposition**: Greatest Common Divisor

## 11.**Proposition**: Relationship Between the Greatest Common Divisor and the Least Common Multiple

## 12.**Definition**: Co-prime Numbers

## 13.**Proposition**: Greatest Common Divisor of More Than Two Numbers

## 14.**Proposition**: Least Common Multiple of More Than Two Numbers