<PRE><B>Question 118433</B>
I&#39;ll do the first one to show you how to get started:





Let&#39;s find all the factors of 165:




First take the square root of 165 to get {{{sqrt(165)=12.85}}}. Now round 12.85 to get 13. This is the number we will stop at.


So let&#39;s ask ourselves...

Is 1 a factor of 165? Since {{{165/1=165}}} results in a whole number, this means 1 and 165 are factors of 165.



Is 2 a factor of 165? Since {{{165/2=82.5}}} does &lt;font size=&quot;4&quot;&gt;&lt;b&gt;not&lt;/b&gt;&lt;/font&gt; result in a whole number, this means 2 is not a factor of 165.



Is 3 a factor of 165? Since {{{165/3=55}}} results in a whole number, this means 3 and 55 are factors of 165.



Is 4 a factor of 165? Since {{{165/4=41.25}}} does &lt;font size=&quot;4&quot;&gt;&lt;b&gt;not&lt;/b&gt;&lt;/font&gt; result in a whole number, this means 4 is not a factor of 165.



Is 5 a factor of 165? Since {{{165/5=33}}} results in a whole number, this means 5 and 33 are factors of 165.



Is 6 a factor of 165? Since {{{165/6=27.5}}} does &lt;font size=&quot;4&quot;&gt;&lt;b&gt;not&lt;/b&gt;&lt;/font&gt; result in a whole number, this means 6 is not a factor of 165.



Is 7 a factor of 165? Since {{{165/7=23.5714285714286}}} does &lt;font size=&quot;4&quot;&gt;&lt;b&gt;not&lt;/b&gt;&lt;/font&gt; result in a whole number, this means 7 is not a factor of 165.



Is 8 a factor of 165? Since {{{165/8=20.625}}} does &lt;font size=&quot;4&quot;&gt;&lt;b&gt;not&lt;/b&gt;&lt;/font&gt; result in a whole number, this means 8 is not a factor of 165.



Is 9 a factor of 165? Since {{{165/9=18.3333333333333}}} does &lt;font size=&quot;4&quot;&gt;&lt;b&gt;not&lt;/b&gt;&lt;/font&gt; result in a whole number, this means 9 is not a factor of 165.



Is 10 a factor of 165? Since {{{165/10=16.5}}} does &lt;font size=&quot;4&quot;&gt;&lt;b&gt;not&lt;/b&gt;&lt;/font&gt; result in a whole number, this means 10 is not a factor of 165.



Is 11 a factor of 165? Since {{{165/11=15}}} results in a whole number, this means 11 and 15 are factors of 165.



Is 12 a factor of 165? Since {{{165/12=13.75}}} does &lt;font size=&quot;4&quot;&gt;&lt;b&gt;not&lt;/b&gt;&lt;/font&gt; result in a whole number, this means 12 is not a factor of 165.





Remember, stop at 13. Notice how the next factor is 15 and it&#39;s already paired with 11 (ie {{{15*11=165}}}). So this shows that any factor greater than 13 will be paired with it&#39;s corresponding factor that is less than 13. This means we only need to test numbers that are less than 13. Essentially this cuts our work in half.




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Answer:

So the factors of 165 are


1, 3, 5, 11, 15, 33, 55, and 165

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