The "primeness" of a positive integer x is defined as the positive difference between its largest and smallest prime factors. Which of the following has the greatest primeness?
A) 10
B) 12
C) 14
D) 15
E) 18
How will i start to solve this? Can any experts help me?
Hi lheiannie07,
Let's take a look at your question.
The question states that the "primeness" of a positive integer x is defined as the positive difference between its largest and smallest prime factors.
To find the greatest primeness, we will find the primeness of each number given one by one by finding its factors.
Primeness of 10:
Factors of 10 = 1, 2, 5, 10
Smallest prime factor = 2
Largest prime factor = 5
Primeness of 10 = 5 - 2 = 3
Primeness of 12:
Factors of 12 = 1, 2, 3, 4, 6, 12
Smallest prime factor = 2
Largest prime factor = 3
Primeness of 12 = 3 - 2 = 1
Primeness of 14:
Factors of 14 = 1, 2, 7, 14
Smallest prime factor = 2
Largest prime factor = 7
Primeness of 14 = 7 - 2 = 5
Primeness of 15:
Factors of 15 = 1, 2, 3, 5, 15
Smallest prime factor = 2
Largest prime factor = 5
Primeness of 15 = 5 - 2 = 3
Primeness of 18:
Factors of 18 = 1, 2, 3, 6, 9, 18
Smallest prime factor = 2
Largest prime factor = 3
Primeness of 18 = 3 - 2 = 1
We can see that 14 has the largest primeness, i.e. 5.
Therefore, Option
C is correct.
Hope this helps.
I am available, if you'd like any follow up.
