SUMMARY ORDER
Petitioner Zalman Segal, seeks review of a May 15, 2006 final order of removal issued by the Board of Immigration Appeals (“BIA”). The order dismisses Se-gal’s appeal from a July 6, 2004 decision of Immigration Judge (“IJ”) Paul A. DeFonzo denying Segal a waiver of inadmissibility pursuant to section 212(c) of the Immigration and Nationality Act, 8 U.S.C. § 1182(c) (repealed). See In re Zalman Segal, No. A36 856 084, 2006 WL 1647440 (B.I.A. May 15, 2006), affg No. A36 856 084 (Immig. Ct. N.Y. City July 6, 2004). We assume the parties’ familiarity with the procedural history, facts, and relevant issues on appeal.
In the absence of a constitutional or legal issue, we do not have jurisdiction to review final orders of removal against aliens deemed by the BIA to be removable for having been convicted of a crime involving moral turpitude. 8 U.S.C. § 1252(a)(2)(C). We also lack jurisdiction to review purely discretionary decisions. Id. § 1252(a)(2)(B)(ii). The REAL ID Act, however, restored our jurisdiction over constitutional claims and questions of law. Id. § 1252(a)(2)(D); Xiao Ji Chen v. U.S. Dep’t of Justice, 471 F.3d 315, 324 (2d Cir.2006) (hereinafter, “Xiao Ji Chen II”). We also retain jurisdiction to determine our own jurisdiction over a petition for review. See Kuhali v. Reno, 266 F.3d 93, 100 (2d Cir.2001).
“To determine whether we have jurisdiction ... we must ‘study the arguments asserted ... [and] determine, regardless of the rhetoric employed in the petition, whether it merely quarrels over the correctness of the factual findings or justification for the discretionary choices’ made by the BIA,” Noble v. Keisler, 505 F.3d 73, 78 (2d Cir.2007) (quoting Xiao Ji Chen II, 471 F.3d at 329 (second and third alterations in original)), or whether instead it raises a colorable (i. e., nonfrivolous) constitutional claim or question of law, Barco-Sandoval v. Gonzales, 516 F.3d 35, 40 (2d Cir.2008). “[A] question of law may ‘arise for example in fact-finding which is flawed by an error of law’ ” — such as where the IJ unambiguously mischaracterizes the record — “or ‘where a discretionary decision is argued to be an abuse of discretion because it was made without rational justification or based on a legally erroneous standard.’ ” *45Gui Yin Liu v. INS, 508 F.3d 716, 721 (2d Cir.2007) (per curiam) (quoting Xiao Ji Chen II, 471 F.3d at 329); accord Khan v. Gonzales, 495 F.3d 31, 35 (2d Cir.2007).
Petitioner first claims that the IJ made factual errors that are so egregious as to amount to errors of law: He contends that two of the IJ’s findings — that he failed to inform New York State of his immigration status when he applied for public assistance and that he lied and equivocated when asked about his criminal past during a 1988 immigration hearing— are belied by unambiguous record evidence to the contrary. Petitioner further contends that the IJ “significantly understated” his length of residence in the U.S. Having studied these arguments and the record, however, we conclude that Petitioner has not identified a question of law but rather has quibbled with the IJ’s fact-finding and his weighing of discretionary factors. Such arguments are insufficient to invoke our jurisdiction.
We also lack jurisdiction to review Petitioner’s second argument, which is that the IJ engaged in “faulty reasoning” when, in weighing the positive and negative equities bearing on Petitioner’s application, he stated that he was “chilled” at Petitioner’s willingness to apply for and procure public benefits in 1999 and that he was further “chilled” by the thought of people subjecting themselves to Petitioner’s hypnotherapy services. Given the context, the IJ’s statements did not amount to an error of law. The IJ’s discussion of Petitioner’s stint on public assistance pertained to Petitioner’s lack of candor on the application, not to his need for public support. The IJ expressed concern about Petitioner’s hypnotherapy practice because of Petitioner’s history of fraud, and, in any case, he made that comment after concluding, on other grounds, that Petitioner was undeserving of a positive exercise of discretion.
Petitioner’s final argument, however, is a legal one, over which we have jurisdiction: he contends that in evaluating his 212(c) application, the IJ misapplied binding BIA precedent regarding how to exercise the Attorney General’s discretion.
When an Immigration Court is faced with a 212(c) petition from an eligible petitioner, it must consider “all the facts and circumstances involved” and “balanc[e] ... the social and humane considerations presented in an alien’s favor against the adverse factors evidencing his undesirability as a permanent resident.” Matter of Edwards, 20 I. & N. Dec. 191, 195 (B.I.A. 1990); accord Lovell v. INS, 52 F.3d 458, 461 (2d Cir.1995). Favorable considerations, according to the BIA, include residence of long duration in the U.S., evidence of hardship to the alien and to his family should deportation occur, a history of employment, “and other evidence attesting to a respondent’s good character.” Matter of Edwards, 20 I. & N. Dec. at 195. Adverse factors include “the nature and underlying circumstances of the exclusion or deportation ground at issue, ... the existence of a criminal record and, if so, its nature, recency, and seriousness, and the presence of other evidence indicative of a respondent’s bad character or undesirability as a permanent resident of this country.” Id.
Contrary to BIA guidance, the IJ characterized as adverse some factors that are not legally relevant to bad character or undesirability as a permanent resident, such as Petitioner’s divorce from his U.S. citizen wife and the fact that his immediate family is in Israel. These findings are relevant to the existence of hardship, a positive equity, but they are not negative equities. In categorizing them as such, the IJ misapplied what we have referred to as a “legal standard,” see, e.g., Khan, *46495 F.3d at 35, and violated the Code of Federal Regulations, see 8 C.F.R. § 1003.1(g) (“[D]ecisions of the Board ... shall be binding on all ... immigration judges in the administration of the immigration laws of the United States.”). And in failing to correct that error on review, the BIA committed an error of law. “While the Board is free to modify its precedents in a reasoned fashion, it acts arbitrarily and unlawfully when it simply ignores established holdings.” Johnson v. Ashcroft, 378 F.3d 164, 171 (2d Cir.2004).
The factors considered were, however, not improperly reviewed; they were simply listed by the IJ on the wrong side of an equation. As a result, we are “confident that the agency would reach the same result upon a reconsideration cleansed of errors” and conclude that a remand in this case would be futile. Lin Zhong v. U.S. Dep’t of Justice, 480 F.3d 104, 117 (2d Cir.2007) (internal quotation marks omitted). The IJ’s most recent decision in this case represents the third consideration of Petitioner’s 212(c) petition and its third determination that, despite the positive equities that Petitioner has presented, he does not deserve a waiver of exclusion.
We have considered all of Petitioner’s arguments. Some quarrel with the IJ’s fact finding and discretionary choices, and so we lack jurisdiction to consider them. The others are without merit. Accordingly, the petition for review is DISMISSED in part and DENIED in part. The pending motion for a stay of deportation/removal is DISMISSED as moot.