To find how many times greater \( 1.365 \times 10^8 \) is than \( 3.5 \times 10^6 \), we divide the first number by the second number:
\[ \frac{1.365 \times 10^8}{3.5 \times 10^6} \]
We can simplify this division by separating the coefficients and the powers of ten:
\[ \frac{1.365}{3.5} \times \frac{10^8}{10^6} \]
Calculating the powers of ten:
\[ \frac{10^8}{10^6} = 10^{8-6} = 10^2 \]
Now we calculate the coefficient:
\[ \frac{1.365}{3.5} \approx 0.39 \]
Now combine these results:
\[ 0.39 \times 10^2 = 0.39 \times 100 = 39 \]
Thus, \( 1.365 \times 10^8 \) is approximately \( 39 \) times greater than \( 3.5 \times 10^6 \).
So, the final answer is:
\[ \boxed{39} \]