Find the number of factors W of 180 that are in the form (4*k + 2), where k is a non-negative integer?  Choose the correct choice from the following options.
A) 1 B) 2 C) 3 D) 4 E) W=6
As for the question, the most straightforward way is to list out the factors (this is fine for this question as 180 is a relatively small number). Number of factors of 180 W(=2^2*3^2*5) = 18. So listing the factors gives us:   1, 180   2, 90   3, 60   4, 45   5, 36   6, 30   9, 20   10, 18   12, 15   As the question asks us about the factors of the form 4k+2 ---&gt; eliminate all ODD factors. You are now left with   2,4,6,10,12,18,20,30,36,60,90,180   For the form 4k+2, the first few values are 2, 6, 10, 14, 18, 22, 26, 30 ... already giving you 5 factors (=2,6,10,18,30). You can stop here and mark 6 (6th one = 90) as the correct answer as 5 is not given.   For checking any particular factor whether they conform to the form 4k+2---&gt; do the following   4k+2 = 36 ---&gt; 4k = 34 --&gt; this will NOT give you an integer value for k ---&gt; reject. Proceed with others until you find all the values asked.   W=6 is thus the correct answer.
<result>E</result>
Find the number of factors W of 180 that are in the form (4*k + 2), where k is a non-negative integer?