general relativity - What is the exact relation between the age of the universe and the cosmological constant?

I understand that the relation between the age $t_0$ of the universe and the cosmological constant $\Lambda $ is something like

$$c t_0 = \frac{f}{\sqrt{\Lambda}}$$

Can somebody provide the precise numerical factor $f$ for the Lambda CDM Model? This does not seem to be explained anywhere. It seems that the factor must be of the order of $f \approx 1.35$. What is the exact expression for this number $f$?

From the answers given below I get a new issue: there an latest Planck-satellite value for $\Lambda $ in $1/{\rm m}^2$? For strange reasons, SI units are rarely used in this particular case.