Carcass wrote:
An integer n that is greater than 1 is said to be "prime-saturated" if it has no prime factor greater than or equal to \(\sqrt{n}\). Which of the following integers is prime saturated?
A) 6
B) 35
C) 46
D) 66
E) 75
So, n is prime saturated if
the largest prime factor of n < √n.
If we square both sides of the inequality, we get: n is prime saturated if (
the largest prime factor of n)² < n
A.
6 = (2)(
3) --->
3² >
6 n is NOT PRIME SATURATED
B.
35 = (5)(
7) --->
7² >
35 n is NOT PRIME SATURATED
C.
46 = (2)(
23) --->
23² >
46 n is NOT PRIME SATURATED
D.
66 = (2)(3)(
11) --->
11² >
66 n is NOT PRIME SATURATED
E.
75 = (3)(5)(
5) --->
5² <
75 n IS PRIME SATURATED
Answer: E