Donald Trump and Theresa May gave a joint press conference at the Prime Minister’s Chequers retreat today.

Mr Trump’s speech sent the twittersphere into meltdown, with many commentators pointing out a number of false or misleading claims from the US President.

Here are four of the biggest ones we spotted.

Claim 1: The Sun left out the “tremendous things” Trump said about Theresa May

Mr Trump did an interview with the Sun newspaper yesterday, in which he appeared to criticise Mrs May’s Brexit approach.

But at this afternoon’s Chequers press conference, he suggested that the paper had left out key details.

He said today: “I didn’t criticise the Prime Minister, I have a lot of respect for the Prime Minister, and unfortunately, there was a story that was done, which was, you know, generally fine, but it didn’t put in what I said about the Prime Minister, and I said tremendous things.”

But a quick glance a page 2 of the Sun this morning would suggest otherwise. The paper said “Trump insisted he still thinks [Theresa May] is ‘a very good person’”.

Later, the same article says: “Asked about a report in The Washington Post that he thinks of Mrs May as ‘a bossy school-teacher’, Mr Trump said: ‘No, no, no, no. I never said anything bad about her. That is fake news. I think she is a nice person, I get along with her very nicely.’”

Today, Mr Trump even suggested that he had recorded the Sun interview to avoid “fake news”. It’s true that the interview is on tape – the Sun released the recording today.

Here’s what Tom Newton-Dunn, the Sun’s political editor who conducted the interview, tweeted today:

As for whether Mr Trump criticised the Prime Minister, that’s up for debate. He did suggest that she had taken the wrong approach with the Brexit negotiations, apparently ignoring his advice. But whether that constitutes a personal attack on Mrs May is not clear.

Claim 2: Trump predicted Brexit the day before the referendum

At today’s Chequers meeting, Mr Trump said: “I was opening Turnberry the day before Brexit and I said ‘I think Brexit will happen’ and it did happen.”

He’s referring to his trip to his own luxury golf club in Scotland. The problem is, he opened the course the day after the Brexit referendum, when the result was already known.

Here’s Mr Trump’s tweet – dated the day after the vote – where he describes having “just arrived in Scotland.”

There were other occasions on which Mr Trump correctly predicted the referendum result before the ballot – so it’s strange that he’s used this example to make his point.

Claim 3: “In Germany we have 52,000 troops, and we have a lot of troops in Europe.”

Not according to the latest figures from the US Defense Manpower Data Center, who say there are 34,821 US service personnel on active duty in Germany.

If you include reservists and civilian staff, you get a grand total of 47,492 Americans in Germany.

There are just over 9,000 US troops active duty personnel in the UK, 12,766 in Italy and 3,680 in Spain.

Some commentators have made the point that pulling US personnel out of overseas bases would not necessarily save President Trump money, since the troops would still have to be paid, housed and supplied on US soil, and foreign countries share the burden of hosting them.

Claim 4: “[the US] were paying 90 per cent of the cost of NATO”

It’s not clear where President Trump is getting his figures from here, but they don’t make a lot of sense.

NATO has civil and military budgets, and America pays 22 per cent of the total cost, worked out by a cost-sharing formula. So the President can’t be talking about this.

Presumably President Trump is talking about the total military spending undertaken by all the countries in NATO – but not all this spending goes on NATO projects.

According to the military alliance’s estimated spending figures for 2017, the US spent $686 billion on defence, much more than any other member state.

If you add together all the money spent by all the countries in NATO, the US figure is 71.5 per cent of the total.

But these figures represent the total military budgets of all the countries, including things that benefit NATO and things that have nothing to do with NATO.

It is true to say, as President Trump has repeatedly in recent days, that only five out of the 29 members are meeting the target of spending at least 2 per cent of their own GDP on defence.

Only the US, Britain, Estonia, Greece and Latvia are hitting the target.