amychen77 wrote:
A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two digit prime saturated integer ?
A. 99
B. 98
C. 97
D. 96
E. 95
Given prime saturated is the product of all the different positive prime factors of \(n\) which is less than the \(\sqrt{n}\).
Checking the answer choices; the highest value is \(99\). \(\sqrt{99}\) is more than \(9\) and less than \(10\).
Lowest value is \(95\). \(\sqrt{95}\) is more than \(9\) and less than \(10\).
Hence the square root of all answer choices are between \(9\) and \(10\).
A. \(99 = 3*3*11\) \(=> 3*11 = 33\)
B. \(98 = 2*7*7\) \(=> 2*7 = 14\)
C. \(97 => 1* 97\)
D. \(96 = 2^5*3\) \(=> 2*3 = 6\). \(=>\) Less than \(\sqrt{96}\).
E. \(95 =>5*19\)
Answer D