{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $p_i = {2, 3, 4, 5, \\dots}$ we continue to divide $c$ by $p_i$. If $c$ becomes 1 then $p_i$ is the greatest prime factor, otherwise we increase $p_i$ by one. We know that any $p_i$ that divides $c$ is prime, because otherwise it would be of the form $p_i = {q_1}^{a_i} \\dotsm {q_n}^{a_n}$ and since $q_i$ is smaller than $p_i$, $c$ would have been already divided by it, so $p_i$ must be a prime number. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6857"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = 600851475143\n",
    "p = 2\n",
    "while c > 1:\n",
    "    if c % p == 0:\n",
    "        c /= p\n",
    "        continue\n",
    "    p += 1\n",
    "p"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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   "name": "python",
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  },
  "title": "Largest prime factor"
 },
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