{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Division euclidienne"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entre le dividende\n",
      "50\n",
      "Entre le diviseur\n",
      "6\n",
      "Le quotient de  50 par  6  est  8\n"
     ]
    }
   ],
   "source": [
    "def quotient (dividende,diviseur):\n",
    "    if (dividende < diviseur):\n",
    "        return 0\n",
    "    else:\n",
    "        return 1 + quotient (dividende - diviseur, diviseur)\n",
    "\n",
    "a=int(input('Entre le dividende\\n'))\n",
    "b=int(input('Entre le diviseur\\n'))\n",
    "print('Le quotient de ',a,'par ',b,' est ',quotient(a,b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PGCD par la méthode des différences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entrer a\n",
      "480\n",
      "Entrer b\n",
      "260\n",
      "Le PGCD de  480  et  260  est  20\n"
     ]
    }
   ],
   "source": [
    "def pgcd(a,b):\n",
    "    while a != b:\n",
    "        if a>b:\n",
    "            a=a-b\n",
    "        else:\n",
    "            b=b-a\n",
    "    return a\n",
    "\n",
    "a=int(input('Entrer a\\n'))\n",
    "b=int(input('Entrer b\\n'))\n",
    "print('Le PGCD de ',a,' et ',b,' est ',pgcd(a,b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PGCD par un algorithme récursif"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entrer a\n",
      "535\n",
      "Entrer b\n",
      "75\n",
      "Le PGCD de  535  et  75  est  5\n"
     ]
    }
   ],
   "source": [
    "def euclide(a,b) :\n",
    "    #calcul du pgcd de a et b\n",
    "    if (b==0) :\n",
    "        return(a)\n",
    "    else :\n",
    "        r=a%b\n",
    "        return euclide(b,r)\n",
    "    \n",
    "a=int(input('Entrer a\\n'))\n",
    "b=int(input('Entrer b\\n'))\n",
    "print('Le PGCD de ',a,' et ',b,' est ',euclide(a,b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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