Trump's NATO claims and more: WEEKLY FACT CHECK Trump's assertions abroad in Belgium and the U.K. call for a few fact checks.

It's been a whirlwind week overseas for the president and at times it looked as though he’d forgotten to pack his facts. He ends his seven-day European trip in Helsinki, Finland, Monday, meeting with Russian President Vladimir Putin. He’ll do so after declaring victory at a NATO summit, claiming he's secured new commitments from allies on defense spending.

That's where ABC's Fact Check Friday begins. (Your fact checker was on holiday last week so we've added one from July 3. But it's worth it. Read to the end.)

They don't pay dues

Arriving in Brussels, Belgium, this week for the NATO summit, President Trump made clear from the start he was not there to play nice - he was there to make other nations pay up.

And he's not wrong to say many members of the alliance are delinquent on their dues – nor is he the first to complain about it. This fact check rules that Trump is justified in his complaints about burden sharing. Still, he gets one big fact wrong.

First – some background on NATO defense spending. It’s an old issue. In 2016, President Obama himself famously derided some European allies as "free riders."

The facts are that all 29 NATO member countries pledged in 2014 to spend at least 2 percent of their gross domestic product on national defense by the year 2024. But according to the latest NATO figures, only five countries have met that goal.

Trump is right when he points to Germany as one NATO nation that hasn’t yet met the NATO pledge to spend 2 percent of GDP on national defense.

But here's where he's wrong. He's said repeatedly that those countries now owe the United States back pay. He said it again on Wednesday to NATO's Secretary General Jens Stoltenberg during a confrontational breakfast meeting. "Frankly, many countries owe us a tremendous amount of money for many years back, where they're delinquent, as far as I'm concerned."

That's not true because that's not how it works. The pledge is to spend money on national defense, not to pay into an account or to another country. These allies are short-changing their own defense, and in turn their ability to jointly defend other NATO nations – including the U.S. That's what's got the president upset. And again, he's not wrong about that.

"They agreed to pay more, and... more quickly"

President Trump also stated, without any evidence, that all NATO members agreed on the last day of the summit to new commitments to defense spending. The problem is that none of those purported new commitments were documented, and there's no evidence NATO members have agreed to pony up any more than previously pledged.

Immediately following an emergency session of the NATO leaders on Thursday to discuss Trump's demands, the president held an unannounced press conference where he completely reversed himself on many of the criticisms he'd had of NATO just hours before, including questioning the value of the alliance itself. It was a remarkable mood swing, and he declared "everybody in the room" agreed "to pay more, and they agreed to pay it more quickly."

He made similar claims 11 times in the press briefing. But the joint communique signed by the 29 NATO members made no mention of increased spending beyond previously agreed upon pledges. No one else in the room backed Trump’s claims either. In fact, according to the Associated Press, French President Emmanuel Macron explicitly denied that NATO members agreed to new spending terms.

Taking attendance- basic facts

Late last month, Health and Human Services Secretary Alex Azar defiantly told lawmakers he could find any child in the department's custody "within seconds," using mere "keystrokes.” But clearly, that's not true, because, within the span of just 10 days, Secretary Azar changed his estimate of immigration children in custody by nearly 1,000 kids.

In a letter to Azar, Senate Democrats noted that, on the same day he testified he could find those children in seconds, and that “there is no reason why any parent would not know where their child is located,” Azar told lawmakers there were 2,047 children in HHS custody. But just nine days later he changed the number drastically, telling reporters that up to 3,000 -- not 2,047 -- were in custody.

Meantime, the Trump administration this week missed a court-ordered deadline to reunite all tender-aged immigrant children it had separated at the border from their families. It was only able to reunite roughly half of those children under 5 years-old. Critics blame disorganization and poor planning.

"I didn't criticize the Prime Minister"

"I didn't criticize the Prime Minister." That's what the president said at a press conference while standing next to the British Prime Minister Teresa May in Chequers, England Friday. Maybe he means he didn't call her any bad names, but he was certainly critical of her political skills.

In a stunning breach of diplomatic protocol, the president had given a politically damaging interview to a tabloid British newspaper that published just after he arrived in the United Kingdom. In it, he attacked May's controversial "soft” Brexit strategy and endorsed her main political rival- Boris Johnson. He resigned as foreign secretary earlier this week over his objection to her plan to leave some trade ties intact with the European Union, setting himself up as a possible contender to replace May.

Boris Johnson "would make a great Prime Minister," Trump told The Sun newspaper. The interview was such cause for alarm when it was released that the president's press secretary Sarah Sanders had to do damage control, issuing a statement clarifying the president's views.

“The President likes and respects Prime Minister May very much. As he said in his interview with the Sun she “is a very good person” and he “never said anything bad about her”. He thought she was great on NATO today and is a really terrific person. He is thankful for the wonderful welcome from the Prime Minister here in the U.K.”

Fake News critic

Hours before tweeting that the Washington Post uses "anonymous sources" the president says "do not exist," the President tweeted a baseless story that appeared on Fox News and in the Daily Mail.

"Just out that the Obama Administration granted citizenship, during the terrible Iran Deal negotiation, to 2,500 Iranians - including to government officials. How big (and bad) is that?" the president said on Twitter.

It's bad because there is no evidence it's true. Neither the White House nor the State Department responded to requests for evidence, and Jeff Prescott, a former senior national security official in the Obama White House, said in an email to ABC "the allegation is absurd and entirely false."

The story first appeared on Iran's state news agency, quoting an Iranian hardliner attacking his own government when he made the unverified allegation.