## Divisibility

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.**Proposition**: Divisibility Laws

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

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

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

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

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

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

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