ST. PAUL  — Republicans trying to take back control of the U.S. Senate are working hard to sear one big number into the brains of voters from Alaska to Arkansas: 90 percent. Or 95 percent. Or 97 percent.

Depending on the state, that’s how often GOP candidates say their incumbent Democratic opponents have voted with President Barack Obama, citing vote scoring conducted by Congressional Quarterly. Those scores are repeated relentlessly in ads, interviews and debates, part of an effort to tie incumbent Democrats to an unpopular president.

The scores are computed based on how often a senator votes with Obama on an issue on which he publicly expressed an opinion. But those include a large number of procedural votes, uncontroversial nominations and votes on which a majority of Republicans also sided with the president.

Democrats argue such a number unfairly boils down their Senate tenure to a subset of votes that give an undersecretary’s unanimous confirmation the same weight as a major policy initiative. The GOP doesn’t buy it, arguing there are still plenty of bad votes to choose from, with those in favor of the president’s health care law chief among them.

“From issue to issue to issue, Kay Hagan has supported President Obama,” said Daniel Keylin, a spokesman for North Carolina Republican nominee Thom Tillis, who is seeking to unseat Hagan, the Democratic incumbent. “She has rubber-stamped every single nominee.”

Consider the case of Minnesota Sen. Al Franken. In his first debate against Mike McFadden, the Republican challenger repeated six times in less than an hour that Franken had voted with Obama “97 percent” of the time during his first term in office.

The Congressional Quarterly vote scores show that on nearly half the votes used to calculate the 97 percent figure, a majority of Republicans joined Franken in siding with the president. One in five was a unanimous vote.

In Arkansas, the super PAC American Crossroads hit Democratic Sen. Mark Pryor for siding with the president 90 percent of the time in an ad featuring a schoolgirl asked to spell Pryor in a spelling bee. Her answer? “O-B-A-M-A.”

“Close enough,” the judges respond in the ad.

The 90 percent or 93 percent score  — the number changes based on the timespan in question — “is not all representative of how Sen. Pryor has voted, his record or his relationship with the priorities of this president,” campaign spokesman Erik Dorey said.

In Pryor’s case, more than three-quarters of the votes on which he sided with the president were confirmation or procedural votes. A majority of GOP senators joined with Pryor on 50 percent of his votes with Obama — a fifth of which were unanimous.

Pryor, like other Democrats, has also responded by playing up his breaks with the president: opposing Obama’s post-Sandy Hook gun control legislation or pushing to begin construction of the Keystone XL pipeline.

Focusing on how an incumbent senator votes with an incumbent president isn’t a new tactic. Hagan unseated Republican Sen. Elizabeth Dole six years ago after branding Dole as having voted too closely with President George W. Bush, saying in a debate that Dole “voting 92 percent of the time with the president … doesn’t work here in North Carolina.”

Those remarks have been a boon for Tillis and his campaign, which is eager to remind voters that Hagan sided with the president 95 percent of the time.

“It really exposes a double standard on the part of Kay Hagan,” Keylin, the Tillis spokesman, said. “If 92 percent didn’t work here back in 2008, 95 percent certainly doesn’t work here in 2014.”

Since she took office in 2009, a majority of GOP senators joined with Hagan 53 percent of the time to cast a vote supportive of Obama’s position.