Britterica Heard appeals her five-month prison sentence, imposed by the district court after it revoked her supervised release for failure to report for mandatory drug testing. She contends that her sentence is procedurally unreasonable, substantively unreasonable, and a violation of her right to equal protection under the law.
I.
In May 2010 Heard was the front seat passenger in a car pulled over by a sher*851iff s officer in Butts County, Georgia. The officer found 1,995 grams of cocaine and 419.56 grams of marijuana in a bag sitting on the car’s backseat. The officer arrested all three of the car’s occupants — Heard, the driver, and the back seat passenger. When the jail officers searched Heard during her intake, they found 39 grams of marijuana hidden in her vagina. In her interview with investigators, Heard explained that the driver was her boyfriend, that she was only along for the ride to Jacksonville, and that she did not know about the drugs in the bag on the backseat. The other two occupants did not contradict her story when investigators interviewed them. The driver and the backseat passenger were charged with two felonies: possession with intent to distribute cocaine, and possession with intent to distribute marijuana. See 21 U.S.C. § 841(a)(1), (b)(l)(B)(ii), (b)(1)(D); 18 U.S.C. § 2. Heard was charged with misdemeanor possession of marijuana. See 21 U.S.C. § 844(a).
Heard pleaded guilty to the misdemean- or in October 2010. Her guidelines range was 0 to 6 months in prison.1 The district court sentenced Heard in March 2011 to one year of probation — with the condition that she participate in a substance abuse program. She did not raise any objections at the sentence hearing and did not appeal the sentence.
Eight months into her probation, in December 2011, Heard’s probation officer filed a petition to revoke her probation. The probation officer alleged that Heard violated mandatory conditions of her supervised release three times: (1) possessing marijuana in September 2011, (2) being arrested for felony shoplifting in November 2011, and (3) being arrested for felony shoplifting in December 2011. At her revocation hearing in February 2012, Heard admitted that she had possessed marijuana during her supervised release, and the court sentenced her to two months imprisonment followed by one year of supervised release.
After Heard served her sentence and began her year of supervised release, her probation officer filed another petition for revocation in May 2012. He alleged that Heard violated the terms of her supervised release this time by: being arrested for felony shoplifting in March 2012,2 and twice failing to submit to required drug testing in April 2012. After the petition was filed, Heard was again arrested for felony shoplifting in July 2012. The officer filed a revocation report that included two Grade B probation violations for violating a state law while on probation, and two Grade C probation violations for failing to report for drug testing. See U.S.S.G. § 7Bl.l(a)(2)-(3).
At the revocation hearing in September 2012, Heard admitted that she had violated the terms of her probation by missing the two drug tests. The government decided not to pursue the other two violations, so Heard had a guidelines range of 3 to 9 months in prison. See id. § 7B1.4(a). Heard’s attorney argued against prison time on two grounds. The first was that Heard had missed the two drug tests because she could not get a ride to the *852probation office. Counsel pointed out that Heard had tested negative in her seven other drug tests. The second asserted ground was that Heard was suffering from depression, and because she had recently become pregnant she had stopped taking her medication. Counsel asked the court, if it did revoke Heard’s probation, “to place her on home detention, at least until the baby is born, to give her a chance to have proper prenatal care at her expense and not at the expense of the government. And also so that the baby may be born in a hospital.” The government agreed that Heard’s mental health issues had played a role in her string of probation violations and did not push for prison time. The district court, however, was “convinced that a period of incarceration [was] appropriate here.”
The district court entered an order revoking Heard’s supervised release. Based on its consideration of the 18 U.S.C. § 8558(a) sentencing factors, the court sentenced Heard to five months in prison. She has not yet served her sentence because the district court granted her motion for release pending appeal.
II.
Heard contends that her sentence is procedurally unreasonable, substantively unreasonable, and a violation of her equal protection rights. All three contentions rely on selected statements from the hearing, taken out of context to create the appearance of error. We address each in turn, quoting from the transcript to provide proper context for the district court’s statements.
A.
Heard contends that her sentence is procedurally unreasonable because the district court based it on an erroneous fact finding. At the revocation hearing, the district court heard both attorneys’ opening statements and then began its questions with the following observation:
[I]t’s been one thing after another since Ms. Heard received very favorable treatment, I think, when she was sentenced on the substantive offense here. She did plead to the indictment, but I think the indictment was drawn — I think she got a good deal, very much so.
And I’m not complaining about that, I signed off on that. But you would think that with that “good deal” — I remember [the prosecutor] talking then that this was her opportunity to get things back on track. And it’s been constantly off track ever since. So how are things going to be different if there is not some period of incarceration?
Heard contends that these statements amount to an erroneous fact finding that she received a favorable plea bargain from the government, when she actually entered her guilty plea without any bargain. She argues that the district court sentenced her to prison time based on its mistaken belief that she received a favorable plea bargain, and concludes that doing so was reversible error.
The parties argue over which standard of review we should apply here. The government argues that Heard failed to object to this issue at the revocation hearing, so we should review for plain error. See United States v. Aguillard, 217 F.3d 1319, 1320 (11th Cir.2000). Heard claims that she did object, and that we should apply our normal abuse-of-discretion standard. See United States v. Register, 678 F.3d 1262, 1266 (11th Cir.2012). We need not decide the issue because Heard’s challenge fails under either standard.
A fact finding cannot make a defendant’s sentence procedurally unreasonable unless the finding was (1) clearly erroneous and *853(2) a basis for the court’s sentence. See United States v. Gonzalez, 550 F.3d 1319, 1323 (11th Cir.2008) (holding that procedural error exists where the district court “selects [the] sentence based on clearly erroneous facts”). Heard has proven neither requisite. First, contrary to Heard’s assertion, the district court did not make a factual finding that she had received a favorable plea deal from the government. The court acknowledged that Heard “did plead to the indictment” without a plea bargain, so it was not under the mistaken impression that Heard received a plea deal. And the court observing that a misdemeanor was “a good deal” for Heard was merely an observation, not a finding of fact. See United States v. Irey, 612 F.3d 1160, 1199 n. 26 (11th Cir.2010) (en banc) (distinguishing a “characterization” from “a finding of fact”). Second, Heard does not identify anything in the record indicating that the court sentenced her to prison time because it believed she originally got “a good deal.” Everything in the record suggests the opposite. The court expressly removed the government’s charging decision from its considerations, saying that it was “not complaining about” the fact that Heard was originally charged with a misdemeanor. And in deciding Heard’s sentence, the court justified the five-month prison term based on its consideration of the guidelines range and the § 3553(a) factors — without mentioning Heard’s original charge, plea, or sentence. Thus Heard’s challenge fails.
B.
Heard contends that her sentence is substantively unreasonable because the district court: (1) imposed her sentence in order to promote her rehabilitation, which is an impermissible basis for imposing a sentence; and (2) misapplied the sentencing factors set out in 18 U.S.C. § 3553(a). In reviewing the substantive reasonableness of Heard’s sentence, we consider the totality of the circumstances and will reverse the district court only for an abuse of discretion. United States v. Shaw, 560 F.3d 1230, 1237 (11th Cir.2009). “A sentence may be substantively unreasonable if a district court unjustifiably relied on any one § 3553(a) factor, failed to consider pertinent § 3553(a) factors, selected the sentence arbitrarily, or based the sentence on impermissible factors.” Id.
First, Heard contends that the district court relied on an impermissible factor by sentencing her to prison so that she could receive treatment for her mental health issues. Sentencing courts cannot impose or lengthen a prison sentence based on the defendant’s rehabilitative needs. See Tapia v. United States, - U.S. -, 131 S.Ct. 2382, 2391, 180 L.Ed.2d 357 (2011) (“Section 3582(a) precludes sentencing courts from imposing or lengthening a prison term to promote an offender’s rehabilitation.”); see also United States v. Bennett, 698 F.3d 194, 197-98 (4th Cir.2012) (holding that Tapia applies to the revocation of probation). But the district court did neither.
At the revocation hearing, the district court quickly made it clear that it was leaning toward giving Heard another prison sentence. Then Heard’s attorney — not the court — raised the issue of rehabilitation by saying “The question, Your Honor, then is how incarceration rehabilitates her.” Counsel argued that prison would set Heard’s rehabilitation back by preventing her from getting help for her mental health issues. The court dismissed that argument. Initially, the court admonished counsel that “we’re not here for a philosophical discussion about rehabilitation and what role incarceration plays in that.” The court then went on to explain why it believed that prison would not negatively *854affect Heard’s rehabilitation. It countered defense counsel’s argument by noting that, “It seems to me that in many ways the argument could be made that a period of incarceration is in her interest and in the interest of the child.”3 Then the court also pointed out that Heard could “hopefully ... get appropriate counseling” for her mental health issues while she was “in a federal facility or under federal jurisdiction.” The court never said that it was sentencing Heard to prison so that she could receive rehabilitative services, or that it was choosing a specific sentence length so that she could receive rehabilitative services. Compare Tapia, 131 S.Ct. at 2385 (holding that a court could not impose a particular sentence length to ensure that the defendant would complete a prison substance abuse program). And when it came time to consider the 18 U.S.C. § 3553(a) factors, the district court did not indicate that rehabilitation was a factor in its decision.
For these reasons, the district court did not err by pointing out, in response to an argument from Heard’s attorney, that a prison term would not negatively affect Heard’s rehabilitation. See id. at 2392 (“A court commits no error by discussing the opportunities for rehabilitation within prison or the benefits of specific treatment or training programs.”). And even if the district court did err, Heard invited that error by arguing that the court should consider her rehabilitation; we are precluded from reviewing invited errors. See United States v. Harris, 443 F.3d 822, 823-24 (11th Cir.2006).
Second, Heard contends that the district court misapplied the § 3553(a) sentencing factors by failing to give proper weight to her mitigating evidence that she suffered from mental health problems.4 Heard recounts the evidence that was presented to the district court, but offers no reason why the weight the district court gave to her mental health issues amounted to an abuse of discretion. See Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 597, 169 L.Ed.2d 445 (2007) (“The fact that the appellate court might reasonably have concluded that a different sentence was appropriate is insufficient to justify reversal of the district court.”). Thus Heard’s challenge fails.
C.
Finally, Heard contends that the district court violated her right to equal protection by giving her a longer sentence because she was a woman. At the revocation hearing, the court made two references to Heard’s unborn child while discussing whether a prison' sentence would deter her from future misconduct. See 18 U.S.C. § 3553(a)(2)(B) (making “adequate deterrence to criminal conduct” a factor to consider at sentencing). First, it asked a rhetorical question: “If she is not incarcerated for some period of time, and I’m *855thinking about the baby too, what’s going to be any different as we go forward.” (Emphasis added.) Later, after Heard’s attorney urged the court to consider “how incarceration rehabilitates her” and argued that prison time would negatively affect Heard’s rehabilitation because she would not receive treatment for her mental health issues, the court responded: “It seems to me that in many ways the argument could be made that a period of incarceration is in [Heard’s] interest and in the interest of the child.” (Emphasis added.) Heard argues that those two statements show that she “received a harsher sentence than a similarly situated male for no other reason than her female gender.”
Neither of those statements shows that the district court would have treated a similarly situated male differently. The statements show a concern with deterring future misconduct for the sake of the child — irrespective of its parent’s gender. The court could have just as easily made the same statements to a single' father with a young child. If a single father’s attorney raised the issue of who would care for the child with the father in prison, the court could acknowledge, as it did in this case, that it was “thinking about the baby” and that “a period of incarceration is in [the father’s] interest and in the interest of the child.” Because the statements do not show that the district court would have treated a father differently, Heard has not made the basic showing needed for an equal protection challenge — that a similarly situated male would have been treated differently. See Weinberger v. Wiesenfeld, 420 U.S. 636, 653, 95 S.Ct. 1225, 1236, 43 L.Ed.2d 514 (1975) (explaining that plaintiff must show “dissimilar treatment for men and women who are ... similarly situated” (quotation marks omitted)). Thus Heard’s challenge fails.
III.
For those reasons we hold that the district court did not err in sentencing Heard to five months in prison.
AFFIRMED.