Sixteen of the last 19 US presidents have played golf — and now, in Donald John Trump, the nation can finally boast the very best of them all.

Well, that’s what he’d like you to believe.

“To say ‘Donald Trump cheats’ is like saying ‘Michael Phelps swims,'” writes Rick Reilly in the new book “Commander in Cheat: How Golf Explains Trump” (Hachette Book Group), out Tuesday. “He cheats at the highest level. He cheats when people are watching and he cheats when they aren’t. He cheats whether you like it or not. He cheats because that’s how he plays golf … if you’re playing golf with him, he’s going to cheat.”

Reilly, a former Sports Illustrated columnist who has played with Trump in the past, spoke to dozens of players — both amateur and professional — to recount some of the president’s worst cons on the course, starting with his declared handicap of 2.8.

In layman’s terms, the lower the handicap, the better the player. Jack Nicklaus, winner of a record 18 major golf titles and generally considered the greatest golfer in the history of the game, has a handicap of 3.4.

Nicklaus’ handicap is listed on the same Golf Handicap and Information Network website used by Trump, where players post their scores.

“If Trump is a 2.8,” writes Reilly, “Queen Elizabeth is a pole vaulter.”

Shortly after he became president, Trump played with Tiger Woods, the current world No. 1 Dustin Johnson and the veteran PGA Tour pro Brad Faxon. Given the quality and profile of his companions, you might have thought Trump would have been on his best behavior. Not so.

On one hole, Trump dunked a shot into the lake, but as his opponents weren’t looking he simply dropped another ball — and then hit that into the water, too.

“So he drives up and drops where he should’ve dropped the first time and hits it on the green,” recalls Faxon.

The actor Samuel L. Jackson has also witnessed the underhanded methods Trump employs, according to Reilly.

“We clearly saw him hook a ball into a lake at Trump National [Bedminster, New Jersey],” he says, “and his caddy told him he found it!”

The boxer Oscar De La Hoya and rocker Alice Cooper have also seen the same shenanigans first hand, while LPGA player Suzann Pettersen, another victim, thinks it’s all down to his caddy “since no matter how far into the woods he hits the ball, it’s in the middle of the fairway when we get there.”

And Trump doesn’t just tamper with his own balls.

During a game with Mike Tirico before Trump was elected, the former ESPN football announcer hit the shot of his life, a 230-yard 3-wood towards an elevated green he couldn’t see. But he knew it was close.

When he got to the putting green, however, Tirico’s ball was nowhere to be seen. Instead, it was 50 feet left of the hole in a bunker.

It made no sense — until Trump’s caddy caught up with him after the round.

“Trump’s caddy came up to me and said, ‘You know that shot you hit on the par 5?’” Tirico says. “‘It was about 10 feet from the hole. Trump threw it in the bunker. I watched him do it.’”

Even Trump’s golf courses lie. As the owner of 14 golf clubs and with his name on another five, Trump has, according to Reilly, been known to wildly exaggerate their standing in course rankings, overvalue them and even play fast and loose with their locations.

At Trump Washington at Lowes Island, there’s a Civil War monument (bearing Trump’s name, obviously) between the 14th and 15th holes, reminding golfers of how many soldiers, from North and South, died at that very spot.

It’s a nice touch, even though several Civil War historians have confirmed that no battle took place anywhere near the memorial.

And what about his course at Bedminster? There’s a plaque there with a quote from the renowned course architect Tom Fazio.

It reads:

This is the best design I’ve ever done.

TOM FAZIO

Except that’s not true, either.

“I don’t believe I said it exactly like that,” Fazio told Reilly.

In a game where etiquette is everything, Reilly reports that Trump never takes his cap off for the end-of-round handshake, nor does he remove it in the clubhouse afterward, presumably for fear of what damage a sweaty round might have done to that hairstyle.

He’s even been known to drive his golf cart onto the putting green, an offense Reilly likens to “hanging your laundry in the Sistine Chapel.”

Quite why Trump cheats is another matter. He is, by all accounts, a very good golfer for his age (even Tiger Woods was impressed) but seems incapable of playing by the rules. Does he even care?

To that, Reilly offers a simple reply.

“Golf,” he writes, “is like bicycle shorts. It reveals a lot about a man.”