Scene on Downing Street as the Prime Minister is set to face a vote of confidence

The Prime Minister is facing a vote of no confidence due to growing discontent among Conservative MPs, stemming from the party gate scandal. The process requires 15% of MPs to write formal letters to trigger the vote. The Prime Minister needs the support of at least half of the MPs to survive the vote, which is conducted via a secret ballot. Discontent is widespread, with MPs from various regions and backgrounds expressing dissatisfaction, primarily due to concerns about the Prime Minister's integrity.

How many Conservative MPs are needed to support the Prime Minister to win the vote?

What is the significance of the 'party gate' allegations mentioned in the text?