Simplify in Steps

You do not need the GCF to simplify. Any factor the top and the bottom share can be divided out, and then you look again. $\frac{40}{60}$: both are even, so halve them, $\frac{20}{30}$. Both are even again: $\frac{10}{15}$. Now both end in 0 or 5, so divide by 5: $\frac{2}{3}$.

Why does this land in the same place as the GCF? Dividing by 2, then 2, then 5 divides by $2\cdot 2\cdot 5$, which is 20, in total, and 20 is the GCF of 40 and 60. The steps just split the GCF into small pieces that are easy to spot.

Stop when the top and the bottom share no factor except 1: 2 and 3 share none, so $\frac{2}{3}$ is finished. Quick checks for a shared factor: both even means 2, both ending in 0 or 5 means 5, and both with digits that add up to a multiple of 3 means 3.