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 < 500?  Pick
A) 4 B) 6 C) 8 D) 10 E) 12
To maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^8 = 256 &lt; 500, then the greatest possible length of integer z is 8.   The answer is 8.
<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 < 500?