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Group of an element can be calculated based on the number of valency electrons present in the atom of the element.

the electron configuration is written - by filling the orbitals and shells - with the electrons the atom has.  Then the number of valency electrons in the outer most shell of the atom, is the group of the atom.

Hydrogen has  1 electron in shell K = 1,  1s1.  Hence it is in group 1.
Chlorine has  7 valency electrons in it. It is in group 7.  It has 17 electrons. as: 1s2,  2s2, 2p6, 3s2, 3p5. 

1 5 1
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