How does a leadership challenge to a UK prime minister work?

The Conservatives currently have 316 members of parliament (MPs) so 48 of them would need to write such letters to challenge May

Prime Minister Theresa May has been left exposed at the top of a government unable to unite over Britain's plans to leave the European Union, after Foreign Secretary Boris Johnson and Brexit Secretary David Davis quit within hours of each other.

Below is an explanation of how May could be removed from office if she has to face a leadership challenge:  What needs to happen for there to be a leadership contest? A leadership challenge can be triggered if 15 percent of members of parliament in May's Conservative Party write a letter to the chairman of the party's so-called “1922 committee.” 

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