*52 SUMMARY ORDER
Defendant-appellant Maria Logan was convicted, following a guilty plea, of conspiracy to commit mail and wire fraud, in violation of 18 U.S.C. § 1349. At sentencing, Logan argued that extraordinary family circumstances and her history as an exemplary foster parent warranted a downward departure, a variance, or both. The district court, however, implicitly denied that motion when it principally sentenced her to twenty-four months’ imprisonment, a sentence within the applicable Guidelines range. We assume the parties’ familiarity with the underlying facts, the procedural history, and the issues on appeal.
On appeal, Logan contends that her sentence was neither procedurally nor substantively reasonable. We apply a reasonableness standard — “a particularly deferential form of abuse-of-diseretion review,” United States v. Cavera, 550 F.3d 180, 187-88 & n. 5 (2d Cir.2008) (en banc) — to both the procedural and substantive sentencing challenges, see United States v. Broxmeyer, 699 F.3d 265, 278 (2d Cir.2012).
A. Procedural Reasonableness
Logan first received a draft plea agreement in May 2011, which included a three-point reduction for acceptance of responsibility. When, by late October 2011, Logan had not accepted that proposed agreement, the government withdrew it and offered a less favorable alternative, with only a two-point reduction for acceptance of responsibility. The government contends that, in the intervening five months, it had been required to prepare for trial and expend certain resources. Logan argues that the district court should have granted her this third-point reduction.
A defendant who “clearly demonstrates acceptance of responsibility for his offense” is eligible for a two-level reduction in the offense level calculation. U.S. Sentencing Guidelines Manual (“U.S.S.G.”) § 3El.l(a). A defendant may receive a third-point reduction if “the defendant has assisted authorities in the investigation or prosecution of his own misconduct by timely notifying authorities of his intention to enter a plea of guilty, thereby permitting the government to avoid preparing for trial and permitting the government and the court to allocate their resources efficiently.” Id. § 3El.l(b). Generally, “a government motion is a necessary prerequisite to the granting of the third point.” United States v. Lee, 653 F.3d 170, 173 (2d Cir.2011) (internal quotation marks omitted); see also U.S.S.G. § 3E1.1 cmt. n. 6 (“[T]he Government is in the best position to determine whether the defendant has assisted authorities in a manner that avoids preparing for trial.... ”).
Absent a government motion, however, a district court’s authority to grant the third point is limited; it may only do so if the government’s motive for not making the motion was unconstitutional or if the government acted in bad faith. See Lee, 653 F.3d at 173; United States v. Sloley, 464 F.3d 355, 360-61 (2d Cir.2006). Logan’s brief on appeal, however, does not allege a constitutional violation or argue bad faith. To the contrary, she argues only that “the Government’s refusal to make a motion was unreasonable under the circumstances.” See App. Br. at 32-33 (emphasis added). After affording “great deference” to the district court, see U.S.S.G. § 3E1.1 n. 5 (“The sentencing judge is in a unique position to evaluate a defendant’s acceptance of responsibility.”), we find no error *53in the decision to limit Logan’s reduction for acceptance of responsibility to two points.
Logan further argues that the district court inadequately explained its reasoning for Logan’s sentence. The district court judge is granted “very wide latitude” to craft an appropriate sentence. Cavera, 550 F.3d at 188. Nevertheless, a court “errs procedurally if it does not consider the § 3553(a) factors, or ... fails adequately to explain its chosen sentence.” Id. at 190 (internal citation omitted). Generally, however, “we presume ... that a sentencing judge has faithfully discharged her duty to consider the statutory factors.” United States v. Fernandez, 443 F.3d 19, 30 (2d Cir.2006).
At sentencing, Logan’s counsel made arguments for both a variance under the statutory factors and a departure under the Guidelines. The government then responded, arguing that no extenuating circumstances warranted a departure or a variance. Finally, after hearing from Logan and others speaking on her behalf, the district court stated on the record that it had considered the presentence report (“PSR”), the arguments of both parties (including their sentencing memoranda), the statements made in court, “together with the factors set forth in Title 18 of United State Code Section 3553.” It also expressly adopted the findings of the PSR in its statement of reasons attached to the judgment. See United States v. Watkins, 667 F.3d 254, 261 (2d Cir.2012) (a district court makes sufficient findings of fact by explicitly adopting the factual findings in the PSR).
A fuller explanation of its reasoning would have been helpful. See United States v. Buissereth, 638 F.3d 114, 116-18 (2d Cir.2011) (although court “should have ... explained its sentence in open court,” affirming sentence because court had stated on record that it had “[taken] into account everything that was said and the records in this case and of course all of [defendant’s counsel’s] eloquent arguments” and adopted PSR findings in the judgment). We do not demand, however, “robotic incantations ... to prove the fact of consideration” of these factors. Fernandez, 443 F.3d at 30 (internal quotation marks omitted). Thus, a failure to address each argument or each factor individually is not itself error. See id. at 30-31.
Logan’s final assertion is that the district court erred by denying certain downward departures for family circumstances and prior good works. See U.S.S.G. §§ 5H1.6, 5H1.11. A district court’s decision not to grant a downward departure is generally not appealable unless the defendant provides “clear evidence of a substantial risk that the judge misapprehended the scope of his departure authority.” United States v. Clark, 128 F.3d 122, 124 (2d Cir.1997) (internal quotation marks and citation omitted). Absent such evidence, we presume that the district court understood its authority to depart. United States v. Stinson, 465 F.3d 113, 114 (2d Cir.2006) (per curiam).
Although Logan argues that, because the district court did not address the departure on the record, there is ambiguity as to whether the district court knew it could depart in this case, she provides no evidence to support that allegation beyond the district court’s silence. That is plainly insufficient to carry her burden. See United States v. Scott, 387 F.3d 139, 143 (2d Cir.2004) (noting that district court “is not obliged to give reasons for refusing to depart” and affirming sentence where counsel had moved for departure at sentencing, government responded, then court sentenced defendant without explicitly addressing the motion); United States v. Lawal, 17 F.3d 560, 563-64 (2d Cir.1994) *54(“[A] district court’s silence concerning its refusal to depart downward does not support an inference that the district court misapprehended its scope of authority.”). Moreover, the parties presented detailed arguments to the district court, orally and in writing, on the family circumstances and Logan’s history as a foster parent, and the record makes clear that the district court considered these arguments. Hence, we conclude that its denial of Logan’s departure motions is not appealable.
For the reasons described above, we conclude that the district court committed no procedural error.
B. Substantive Reasonableness
Logan also argues that her twenty-four month sentence was substantively unreasonable. This challenge also fails. Our review for substantive reasonableness is “particularly deferential.” Broxmeyer, 699 F.3d at 289. We will only set aside a district court’s substantive determination in exceptional cases, see Cavera, 550 F.3d at 189, and only then if the sentence is “shockingly high, shockingly low, or otherwise unsupportable as a matter of law,” Broxmeyer, 699 F.3d at 289 (quoting United States v. Rigas, 583 F.3d 108, 123 (2d Cir.2009)).
This is not such a case. The Guidelines range, as calculated by the district court was twenty-four to thirty months’ imprisonment. Logan played a minor role in the mortgage fraud conspiracy, but she still secured five fraudulent mortgages, resulting in a loss of nearly $800,000, and was personally paid $27,000 for her services. She also fraudulently refinanced her home and submitted fraudulent tax returns, neither of which formed part of the offense conduct. Moreover, as discussed above, the record demonstrates that the district court weighed Logan’s family circumstances, her work as a foster parent, and other mitigating factors before deciding to impose a sentence at the bottom of the Guidelines range. Although a Guidelines sentence is not presumptively reasonable, see Cavera, 550 F.3d at 190, under the circumstances here, the twenty-four month sentence was not shockingly high or otherwise unsupportable as a matter of law. Thus, we conclude that Logan’s sentence was substantively reasonable.
We have considered Logan’s remaining arguments and conclude they are without merit. For the foregoing reasons, we AFFIRM the judgment of the district court.