Puzzletime...

To ease into the week, a problem I adapted from one seen over at the 7puzzle blog site:

From the numbers 1-37, find the five integers that remain when you eliminate the following:

1)  any integers containing a 1
2)  prime numbers
3)  factors of 72
4)  numbers divisible by 3 or 5

Once you have the five 'finalists,' eliminate those number pairs that add up to 60.  Then, what number is left?
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.answer below
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ANSWER:  22