Why does chlorine has valency 1 and carbon has valency 4?

Chlorine has valency 1

1. Chlorine has an atomic number of 17 which means its electronic configuration is $2,8,7$.
2. Chlorine has a total of 7 valence electrons in its outermost shell.
3. From this configuration, we can see that chlorine needs only 1 electron to be stable.

Carbon has a valency of 4:-

1. Carbon has an atomic number of 6 which means its electronic configuration is $2,4$.
2. Carbon has a total of 4 valence electrons in its outermost shell.
3. From this configuration, we can see that carbon needs only 4 electrons to be stable.

Therefore, Chlorine needs only 1 electron to be stable, whereas Carbon nee 4 electrons, this is why chlorine has valency 1 and carbon has valency 4.