The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 3000? Pick:
A) 7
B) 9
C) 11
D) 13
E) 15
To maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^11 = 2048 &lt; 3000, then the greatest possible length of integer z is 11.   The answer is 11.
<result>C</result>
The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 3000?