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<html><table height="500" width="1000" border="2"><TR height="5" width="1000"><strong><center><marquee><font color="Green"><h1>APTITUDE</h1></center></strong></font></TR></marquee><TR><TD align="left" width="200" valign="top"><table><TR><a href="numbers.html"><strong>Numbers</strong></a></TR><br><TR><a href="hcf.html"><strong>H.C.F and L.C.M</strong></a></TR><br><TR><a href="dec.html" target="right"><strong>Decimal Fractions</strong></a></TR><br><TR><a href="simplification.html"><strong>Simplification</strong></a></TR><br><TR><a href="squareandcuberoot.html" target="right"><strong>Square and Cube roots</strong></a></TR><br><TR><a href="average.html" ><strong>Average</strong></a></TR><br><TR><a href="pnumbers.html" ><strong>Problems on Numbers</strong></a></TR><br><TR><a href="problemsonages.html"><strong>Problems on Ages</strong></a></TR><br><TR><a href="surdsandindices.html"><strong>Surds and Indices</strong></a></TR><br><TR><a href="percent.html" target="right"><strong>Percentage</strong></a></TR><br><TR><a href="profitandloss.html" target="right"><strong>Profit and Loss</strong></a></TR><br><TR><a href="ratioandproportion.html" target="right"><strong>Ratio And Proportions</strong></a></TR><br><TR><a href="partnership.html"><strong>Partnership</strong></a></TR><br><TR><a href="chainrule1.html"><strong>Chain Rule</strong></a></TR><br><TR><a href="timeandwork.html" target="right"><strong>Time and Work</strong></a></TR><br><TR><a href="pipesandcisterns.html" target="right"><strong>Pipes and Cisterns</strong></a></TR><br><TR><a href="timeanddistance.html"><strong>Time and Distance</strong></a></TR><br><TR><a href="trains.html" target="right"><strong>Trains</strong></a></TR><br><TR><a href="boats.html"><strong>Boats and Streams</strong></a></TR><br><TR><a href="alligation.html"><strong>Alligation or Mixture </strong></a></TR><br><TR><a href="simple.html" target="right"><strong>Simple Interest</strong></a></TR><br><TR><a href="CI.html" target="right"><strong>Compound Interest</strong></a></TR><br><TR><a href=""><strong>Logorithms</strong></a></TR><br><TR><a href="areas.html" target="right"><strong>Areas</strong></a></TR><br><TR><a href="volume.html" target="right"><strong>Volume and Surface area</strong></a></TR><br><TR><a href="races.html" target="right"><strong>Races and Games of Skill</strong></a></TR><br><TR><a href="calendar.html" target="right"><strong>Calendar</strong></a></TR><br><TR><a href="clocks.html" target="right"><strong>Clocks</strong></a></TR><br><TR><a href="" target="right"><strong>Stocks ans Shares</strong></a></TR><br><TR><a href="true.html" target="right"><strong>True Discount</strong></a></TR><br><TR><a href="banker1.html" target="right"><strong>Bankers Discount</strong></a></TR><br><TR><a href="oddseries.html" target="right"><strong>Oddmanout and Series</strong></a></TR><br><TR><a href=""><strong>Data Interpretation</strong></a></TR><br><TR><a href="probability.html"><strong>probability</strong></a></TR><br><TR><a href="percom1.html" target="right" ><strong>Permutations and Combinations</strong></a></TR><br><TR><a href="pinkivijji_puzzles.html" target="right"><strong>Puzzles</strong></a></TR></table></TD><TD valign="top"><a href="numbers.html"><b>BACK</b></a><h2 align="center"><u><b><i>NUMBER SYSTEMS</i></b></u></h2><br><h3>Natural Numbers:-</h3>All positive integers are natural numbers.<br> Ex 1,2,3,4,8,......<br><br>There are infinite natural numbers and number 1 is the least natural number.<br>Based on divisibility there would be two types of natural numbers. They are<br><br>Prime and composite.<br><h3>Prime Numbers :-</h3>A natural number larger than unity is a prime number if it <br>does not have other divisors except for itself and unity.<br><b>Note:-</b>Unity i e,1 is not a prime number.<br><br><i><b>Properties Of Prime Numbers:-</b></i><br>->The lowest prime number is 2.<br>->2 is also the only even prime number.<br>->The lowest odd prime number is 3.<br>->The remainder when a prime number p>=5 s divided by 6 is 1 or 5.However, <br>if a number on being divided by 6 gives a remainder 1 or 5 need not be prime. <br><br>->The remainder of division of the square of a prime number p>=5 divide by 24 is 1.<br><br>->For prime numbers p>3, p虜-1 is divided by 24.<br><br>->If a and b are any 2 odd primes then a虜-b虜 is composite. Also a虜+b虜 <br>is composite.<br><br>->The remainder of the division of the square of a prime number p>=5 divided<br> by 12 is 1. <br><br><i><b>Process to Check A Number s Prime or not:-</b></i><br><br> Take the square root of the number.<br><br>Round of the square root to the next highest integer call this number as Z.<br><br> Check for divisibility of the number N by all prime numbers below Z. If there <br><br>is no numbers below the value of Z which divides N then the number will be prime.<br><br><b>Example</b> 239 is prime or not?<br><br> 鈭?? 快捷鍵說明
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