Rachel Casey pled guilty to one count of wire fraud, in violation of 18 U.S.C. § 1343, and was sentenced to six months of imprisonment. She now challenges the sentence as procedurally and substantively unreasonable. For the reasons that follow, we affirm.
I.
In 2010, an officer conducted a traffic stop of a car being driven by Miiya Brown. Casey was a passenger. During the stop, the officer learned that the vehicle had been stolen. Upon search of the vehicle, the officer found numerous receipts containing various names and handwritten notes with names and identifiers of individuals other than the occupants. An additional search revealed numerous counterfeit drivers’ licenses, debit cards, and checks in various names. The women had obtained identifying information of other individuals and used their own photographs to create counterfeit documents that allowed them to obtain lines of credit and purchase items at various stores.
Casey pled guilty to one count of wire fraud. The probation office calculated a total offense level of eleven and a criminal history category of I, so the advisory guidelines range was eight to fourteen months of imprisonment. The presen-tence investigation report (“PSR”) erroneously indicated that the charge was a Class B felony and thus, that Casey was not eligible for probation. Neither party caught the mistake. Casey filed a sentencing memorandum asking for a probationary sentence. The United States filed a response indicating it believed a sentence of probation was unlawful because the offense was a Class B felony. It also objected to a sentence of probation generally, “based on the defendant’s conduct.”
*813At sentencing the court granted the government’s motion for downward departure, departing three levels, resulting in an adjusted guidelines range of zero to six months. Casey’s attorney requested a sentence of two days of confinement followed by five years of supervised release, apparently believing that Casey was ineligible for probation. After hearing the parties’ arguments, the court sentenced Casey to six months of imprisonment, explaining that a more lenient sentence, including probation, would not “fulfill the need of retribution.”
Casey’s attorney asked the court to explain its reasons for imposing a sentence in the high end of the guidelines range, and the district court responded:
The Court considered this offense, one involving fraud, deception, dishonesty, a lot of planning. And the Court was faced with a defendant who could make choices in her life, and the defendant chose to engage in actions that amounted to fraud and deception. And the Court concluded that a sentence of four months, five months, three months, two months, one month, or zero months would not be sufficient to satisfy the criteria set forth in Section 3553(a).
Casey’s attorney objected on the record that the court “may not have weighed the 3553(a) factors accordingly ... because of [Defendant’s] background and total lack of criminal history.”
II.
Appellate courts review a district court’s sentence under a deferential abuse of discretion standard. Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007).
III.
A district court commits procedural error by failing to properly calculate the guidelines range, treating the range as mandatory, selecting the sentence based on clearly erroneous facts, failing to consider the sentencing factors in 18 U.S.C. § 3553(a), or failing to adequately explain the chosen sentence. Id.
A.
Casey argues that the district court erred procedurally by failing to adequately consider the sentencing factors in § 3553(a) and by putting unreasonable weight on one of the factors. She believes that the district court considered only the nature of the offense and failed to consider her personal characteristics and circumstances. For example, the district court explained that it finds white collar criminals particularly unsympathetic because they are typically educated and relatively financially stable, meaning they make a conscious choice to engage in criminal activity despite having other options. Casey argues this generalization does not apply to her, as she was struggling financially due to unemployment when she committed the crime and was a single mother — factors the district court failed to discuss. Casey also believes the court failed to consider that she played a relatively minor role in the offense, and she argues that she was recruited by a co-defendant and “instructed” on how to carry out the crime. Finally, Casey alleges that the district court focused on the need for retribution, to the exclusion of all other sentencing factors.1
While the district court did not discuss on the record Casey’s status as a single *814mother or the fact that she was unemployed when she committed the crime, this does not mean it did not consider those factors. Additionally, a district court is not required to sentence at the low end of the guidelines range simply because a co-defendant may be more culpable. While the district court focused on retribution, it also considered other factors. Therefore, we cannot say the district court committed an abuse of discretion.
The district court explicitly discussed “the nature and circumstances of the offense” and “the need for the sentence imposed to reflect the seriousness of the offense, to promote respect for the law, and to provide just punishment for the offense.” See 18 U.S.C. § 3558(a)(1), (a)(2)(A). It also briefly mentioned “incapacitation” 2 and rehabilitation and explicitly listed “deterrence” as a sentencing factor, opining that a crime such as this — one that is “thought out,” “planned,” and involves “deception” and “manipulation”— “ought to be subject to deterrence.”
The court also considered Casey’s personal situation. It stated that it “look[s] at the whole person” when deciding on a sentence and “takes into account the personal circumstances and needs and background and characteristics of each defendant.” Casey’s attorney filed a sentencing memorandum, addressing the mitigating aspects of Casey’s personal situation. Attached to the memorandum were several letters written on behalf of Casey. The court specifically noted on the record that it received these letters before sentencing and made them an attachment to the PSR. It also noted that Casey is intelligent, that she “stay[ed] in a civil engineering course for two years,” and thus that she “could have done other things” but “chose to commit crimes instead.” While these may not be the personal circumstances Casey wishes the court would have focused on, we cannot say that it did not consider her personal characteristics at all.
The court also considered Casey’s circumstances and characteristics when deciding to grant the three-level departure. Casey’s attorney, in support of the request for a three-level departure, reminded the court that Casey took responsibility for her actions in a timely manner, assisted the government in the case against her co-defendants, had no criminal history, was an honor student in school, and was currently employed. In response, the court stated, “Based on the government’s motion ... and also the comments of counsel, the Court will grant the government’s motion, and will depart downward ...” (emphasis added).
In sum, although the court could have discussed Casey’s personal characteristics and the sentencing factors in more detail, the record demonstrates that it did consider both. It simply did not find that, in light of the nature of the crime and the need for just punishment and deterrence, her personal circumstances warranted the sentence she desired.
B.
Next, Casey argues that the district court failed to adequately explain its reason for rejecting her request for a sentence of either “straight probation” or a one-to-two-day period of incarceration followed by supervised release. She suggests that the court failed to respond to the arguments she presented at sentencing in favor of a more lenient sentence. “[Wjhen a defendant raises a particular argument in seeking a lower sentence, the record must reflect both that the district *815judge considered the defendant’s argument and that the judge explained the basis for rejecting it.” United States v. Jones, 489 F.3d 243, 251 (6th Cir.2007) (quotation marks and citation omitted).
“ [Although the district court is required to ‘give the reasons for its sentence,’ it is not required to ‘give the reasons for rejecting any and all arguments by the parties for alternative sentences,’ particularly those that are ‘conceptually straight forward.’” United States v. King, 430 Fed.Appx. 514, 518-19 (6th Cir.2011) (quoting United States v. Vonner, 516 F.3d 382, 387-88 (6th Cir.2008)). Moreover, a “district court’s failure to address each argument head-on will not lead to automatic vacatur.” United States v. Liou, 491 F.3d 334, 339 n. 4 (6th Cir.2007). The correct inquiry is “whether ‘[t]he record makes clear that the sentencing judge listened to each argument,’ ‘considered the supporting evidence,’ [and] was ‘fully aware’ of the defendant’s circumstances and took ‘them into account’ in sentencing [her].” Vonner, 516 F.3d at 387 (quoting Rita v. United States, 551 U.S. 338, 358, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007)).
Casey’s arguments for a more lenient sentence (low risk of recidivism, no prior criminal history, and the need to care for her son) were “conceptually straightforward,” and the district court was familiar with these types of arguments. See id. Thus, it was not required to give specific reasons for rejecting each argument. The court listened to the arguments and was aware of the defendant’s circumstances. It read the letters and sentencing memorandum that discussed Casey’s personal characteristics. The court could have explained in more detail its reasons for rejecting Casey’s arguments for a lower sentence, but viewing the record as a whole, we cannot say that its failure to say more amounts to procedural unreasonableness. See Rita, 551 U.S. at 359, 127 S.Ct. 2456 (“We acknowledge that the judge might have said more. He might have added explicitly that he had heard and considered the evidence and argument ... that he found that [the defendant’s] personal circumstances here were simply not different enough to warrant a different sentence. But context and the record make clear that this, or similar, reasoning underlies the judge’s conclusion.”).
C.
Finally, on the issue of procedural reasonableness, Casey argues the district court erred by failing to consider probation as a sentencing option. Both the PSR and the government’s response to Casey’s sentencing memorandum stated that Casey pled guilty to a Class B felony. Casey argues on appeal (and the government agrees) that she actually pled guilty to a Class C felony. The difference is that a sentence of “straight probation” is not an option for Class B felonies, but it is for some Class C felonies. See 18 U.S.C. § 3561(a). Because Casey did not identify the mistake below, she can prevail on appeal only if the district court committed plain error in failing to correct the mistake.
Specifically, she argues that the error affected her substantial right to a fair sentence because the district court relied on erroneous information. She is, however, speculating that the district court did not impose probation because it thought it lacked the authority to do so. While the government’s response to Casey’s sentencing memorandum stated its position that a sentence of probation was unlawful, Casey continued to take the position that probation was a lawful option, and she argued for a one-to-two-day period of confinement in the alternative. Thus, according to the record, a sentence of probation was still an *816argued-for option going into the sentencing hearing.
Additionally, the court knew it could sentence Casey to probation. It stated, “Ms. Casey asked that she be given a probationary sentence. The Court determines that a probationary sentence in this case would not fulfill the need of retribution .... [A] probationary sentence would not be adequate to comply with the purposes set forth in Section 3553(a).” This statement suggests the court considered the option of a probationary sentence and rejected it. Thus, to the extent the district court erred by failing to correct the PSR, such error was harmless.
IV.
Casey also challenges the substantive reasonableness of her sentence, arguing that (1) the sentence was greater than necessary to achieve the purposes of the sentencing factors and (2) the court selected the sentence arbitrarily by failing to consider the relevant factors and gave unreasonable weight to the need for retribution. Because her sentence was below the advisory guidelines range and within the adjusted range, it is presumed to be substantively reasonable. See United States v. Polihonki, 543 F.3d 318, 322 (6th Cir.2008).
In support of her argument that the sentence was greater than necessary, Casey raises the same arguments she raised before the district court in her sentencing memorandum, articulating how she believes the § 3553(a) factors apply to her. A defendant’s “mere allegation that the sentence imposed is greater than necessary to achieve the goals of punishment outlined in § 3553(a) is insufficient to rebut the presumption of reasonableness,” United States v. Dexta, 470 F.3d 612, 616 (6th Cir.2006), and “[t]he fact that [we] might have reasonably concluded that a different sentence was appropriate is insufficient to justify reversal of the district court.” United States v. Bolds, 511 F.3d 568, 582 (6th Cir.2007) (quotation marks and citation omitted). Nothing in the record suggests that the district court’s decision to impose a sentence at the high end of the guidelines range was unreasonable, and Casey’s desire for a more lenient sentence, without more, does not justify reversal.
Her second argument is merely a restatement of her “procedural error” arguments. For reasons discussed above, the district court did not unreasonably weigh the sentencing factors. While it did focus on “the need for the sentence imposed to reflect the seriousness of the offense, to promote respect for the law, and to provide just punishment for the offense,” see 18 U.S.C. § 3553(a)(2)(A), it did implicitly and explicitly reference other factors. “A district court does not necessarily commit reversible error by attaching great weight to any single factor.” United States v. Pizzino, 419 Fed.Appx. 579, 585 (citing Gall v. United States, 552 U.S. 38, 56-57, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007)).
In sum, the district court sentenced Casey within the guidelines range, and although it could have addressed more of the sentencing factors and its rationale on the record, its decision to sentence her at the high end of the guidelines range is not an abuse of discretion.
V.
For the reasons stated above, we AFFIRM.
. The district court explained that it characterizes the factor in § 3553(a)(2)(A), "the need for the sentence imposed to reflect the seriousness of the offense, to promote respect for the law, and to provide just punishment for the offense” as "retribution.”
. Presumably, the district court was referring to the need "to protect the public from further crimes of the defendant,” in § 3553(a)(2)(C).