To determine how many times greater \( 3 \times 10^8 \) is compared to \( 3 \times 10^2 \), we can set up a simple division:
\[ \text{Factor} = \frac{3 \times 10^8}{3 \times 10^2} \]
The \( 3 \)'s will cancel out:
\[ \text{Factor} = \frac{10^8}{10^2} = 10^{8-2} = 10^6 \]
Now, \( 10^6 \) equals \( 1,000,000 \).
Thus, \( 3 \times 10^8 \) is 1,000,000 times greater than \( 3 \times 10^2 \).