For any positive integer n, pi(n) represents the number of factors of n, inclusive of 1 and itself. If a and b are prime numbers, then pi(a) + pi(b) - pi(a x b) =
a)-4 b)-2 c)0 d)-2 e)4
Solution:The only factors of a prime number are 1 and itself. Hence, pi(any prime number) = 2. So, pi(a) = 2 and pi(b) = 2, and therefore pi(a) + pi(b) = 2 + 2 = 4.
Now, the factors of ab are 1, a, b, and ab itself. Hence, the total number of factors of a x b is 4.In other words, pi(a x b) = 4.Hence, pi(a) + pi(b) - pi(a x b) = 4 - 4 = 0.
The answer is C.
My Question : Before I looked at the answer, I used different prime numbers but to no avail. However,in the solution, they use the same prime number which is 2 to solve the problem. Why? Is there something that I'm not understanding here?
Thank you.
a)-4 b)-2 c)0 d)-2 e)4
Solution:The only factors of a prime number are 1 and itself. Hence, pi(any prime number) = 2. So, pi(a) = 2 and pi(b) = 2, and therefore pi(a) + pi(b) = 2 + 2 = 4.
Now, the factors of ab are 1, a, b, and ab itself. Hence, the total number of factors of a x b is 4.In other words, pi(a x b) = 4.Hence, pi(a) + pi(b) - pi(a x b) = 4 - 4 = 0.
The answer is C.
My Question : Before I looked at the answer, I used different prime numbers but to no avail. However,in the solution, they use the same prime number which is 2 to solve the problem. Why? Is there something that I'm not understanding here?
Thank you.
