x is the smallest integer greater than 1000 that is not prime and that has only one factor in common with 30!. What is x?	Choose the most appropriate option.
A) 1009  B) 1021  C) 1147  D) 1273  E) 50! + 1
Next, x and 30! have only one factor in common means that this factor must be 1 (any two integers have 1 as a common factor). Thus no other factor of 30! is a factor of x. So, the least prime of x can be 31 (30! has all primes less than 30).   x cannot be 31*31= 
<gadget id="calculator">31*31</gadget>
<output>961</output>
961 because it's less than 1,000.   The next prime is 37: 31*37= 1147 &gt; 1,000.   Answer: 1147
<result>C</result>
x is the smallest integer greater than 1000 that is not prime and that has only one factor in common with 30!. What is x?