Group theory

Question

Let $G$ be a finite group with sub group $H$ & $K$ such that $|H|=7$ and $|K|=31$ then find $| H  ⋂ K|$

Comments

1? As | H intersection K| should divide order of hours as well as k and as h and k are prime. So only. Number that divides is 1

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yes if two subgroups are mutually prime then there intersection is 1 and that element is identity.

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Yeah, it must be 1.

Answer 1

As,  $gcd(7,31) = 1$

then, $|H⋂K| = 1$