Final answer:
The smallest possible value of |a - b| can be found by considering the values of a and b and choosing factors of the prime factorization of 4214784 that have opposite parity. The smallest possible value of |a - b| is 33850.
Step-by-step explanation:
The smallest possible value of |a - b| can be found by considering the values of a and b. Since a and b have opposite parity, one of them must be even and the other must be odd. We are given that ab = 4214784, so we need to find two numbers whose product is 4214784 and have opposite parity.
The prime factorization of 4214784 is 2^8 * 131^2. To find two numbers whose product is 4214784 and have opposite parity, we can choose one factor of 2 (since it is even) and any factor of 131 (since it is odd). This gives us the numbers 2 * 131 = 262 and 2^7 * 131 = 34112.
Now we can compute the smallest possible value of |a - b| by comparing these two numbers. |262 - 34112| = 33850, so the smallest possible value of |a - b| is 33850.