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Find the number of factors of 180 that are in the form (2k+2), where k is a positive integer.

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Re: Find the number of factors of 180 that are in the form (2k+2), where k is a positive integer.

by Scott@TargetTestPrep » Tue Feb 23, 2021 3:37 pm
AAPL wrote: ↑
Wed Feb 17, 2021 10:00 am
 E-GMAT

Find the number of factors of 180 that are in the form (2k+2), where k is a positive integer.

A. 6
B. 7
C. 11
D. 12
E. 18

OA C
Solution:

Since 2k + 2 is always even, we only need to deal with the even factors of 180. Furthermore, since k is a positive integer, the least value of 2k + 2 is 2(1) + 2 = 4. That is, we are only looking for the even factors of 180 that are greater than or equal to 4.

Since 180 = 1 x 180 = 2 x 90 = 3 x 60 = 4 x 45 = 5 x 36 = 6 x 30 = 9 x 20 = 10 x 18 = 12 x 15, we see that there are 11 such factors (they are in bold).

Answer: C

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