1. Analyze the Relationship Between the Numbers

The first step is to notice the relationship between the two numbers:

$$
\(80,004=2 \times 40,002\)
$$

2. Determine the Prime Factors
- For $x$ (Greatest prime factor of 40,002): We factor 40,002:

$$
\(\begin{gathered}
40,002=2 \times 20,001 \\
20,001=3 \times 6,667 \\
6,667=59 \times 113
\end{gathered}\)
$$


The prime factors are $\(\{2,3,59,113\}\)$. The greatest is 113 .
- For $y$ (Greatest prime factor of 80,004 ): Since $\(80,004=2 \times 40,002\)$, the prime factorization of 80,004 is:

$$
\(80,004=2 \times(2 \times 3 \times 59 \times 113)=2^2 \times 3 \times 59 \times 113\)
$$


The distinct prime factors are $\(\{2,3,59,113\}\)$. The greatest is $\(\mathbf{1 1 3}\)$.
3. Compare Quantity A and Quantity B
- Quantity A (x): 113
- Quantity B (y): 113