The diagram has a scale of 1cm to 4km as the problem said, then we can write
![1\operatorname{cm}\colon4\operatorname{km}]()
If we want to find the scale factor, we must put 4km in cm, it will be 400000 cm, therefore
![1\operatorname{cm}\colon400000\operatorname{cm}]()
Now we have them in the same units, we can "cut" the units on both sides, and we have
![1\colon400000](https://img.qammunity.org/2023/formulas/mathematics/college/kynb5erkqrrcpfm5ddxoaqpy3ezaunxfw7.png)
We can also write it as a fraction:
![\text{scale factor=}(1)/(400000)](https://img.qammunity.org/2023/formulas/mathematics/college/yuoj2c0s4x8e5iylqmttdlke2sfs0n00hq.png)