Question 722997
The range of possibilities is very limited.  Some or the possibilities to first consider could be from the set of {62,63,64,65,66,67,68,69,70,71,72}.  It is a COMPOSITE number, so eliminate the primes.   Look in {62,63,64,65,66,68,69,70,72}.  


Sum of the digits is prime!  This cuts down the possibilities to {65,70}.  6+5=11 prime, and 7+0=7 prime.  


FOUR FACTORS?  Cannot be 65 because this one only has 5 and 13 as its factors.  The number must be 70 to satisfy all three conditions. 70=7*10 and 70=35*2, but the condition is still not a fit because also 70=14*5.  If you were to rely on a very simple elementary way of thinking, you could choose 65 because in the very elementary sense, the factors of 65 are: 1, 5, 13, and 65.

ANSWER: Must be 65.