LOGAN, Circuit Judge.
Codefendants Michael Sardin and Oscar St. Julian were convicted for maintaining a premises for the purpose of distributing cocaine base, in violation of 21 U.S.C. § 856. In these appeals, Sardin and St. Julian challenge their sentences following the resentencing ordered by this court in United States v. Sardin, 921 F.2d 1064 (10th Cir.1990), and United States v. St. Julian, 922 F.2d 563 (10th Cir.1990). We consider defendants’ appeals as raising two issues: first, did the district court adequately explain the reasonableness of the degree of its upward departure; and second, did the district court comply with the mandate of this court in Sardin, 921 F.2d at 1067, by resentencing both Sardin and St. Julian to seventy-two months, when co-defendant Kelvin Davis was sentenced to thirty-six months for the same crime.
I
Sardin, St. Julian and Davis were all convicted for the same crime of maintaining a crackhouse. The presentence reports calculated Davis’ and defendants’ offense levels, criminal history categories, and guidelines sentences as follows:
See St. Julian, 922 F.2d at 565; United States v. Davis, 912 F.2d 1210, 1211 (10th Cir.1990); II Sardin R. 4-5; II St. Julian R. 4. The district court originally departed upward from the recommended guidelines sentences on the basis that the guidelines did not adequately account for the large quantity of drugs involved in the case. Accordingly, Sardin was sentenced to 120 months in prison; St. Julian was sentenced to 72 months in prison; and Davis was sentenced to 36 months in prison. Each of the defendants appealed their sentences. Applying the three-part test found in United States v. White, 893 F.2d 276, 277-78 (10th Cir.1990), and refined in United States v. Jackson, 921 F.2d 985, 989-90 (10th Cir.1990) (en banc), we remanded and ordered resentencing for both Sardin and St. Julian. See Sardin, 921 F.2d at 1068; St. Julian, 922 F.2d at 572. We affirmed Davis’ sentence after requiring the district court to explain its reasons for the degree of departure from the guidelines. See United States v. Davis, 922 F.2d 616, 617-18 (10th Cir.1990).
In Sardin’s first appeal we agreed with the district court that the quantity of drugs was an appropriate basis for departing upward from the sentencing guidelines. Sardin, 921 F.2d at 1066. Nevertheless, after comparing Sardin’s original sentence with the sentences given his codefendants, we held the degree of departure from the guidelines in Sardin’s sentencing “inexplicable given the facts in the record.” Id. at 1067. “The basis for Sardin’s apparently disproportionate sentence [was] unclear.” Id. at 1066. Concluding that “the three defendants here were ‘similar offenders’ engaged in ‘similar criminal conduct’ with respect to the reason given for their upward departure,” we reasoned that “they should have received equivalent upward departures.” Id. at 1067.
Similarly, in St. Julian’s first appeal, we affirmed the district court’s basis for upward departure — the large amount of drugs involved. St. Julian, 922 F.2d at 569. We vacated and remanded for resen-tencing, however, because we held that the district court had not explained how it arrived at St. Julian’s sentence, which caused us to be unable to review the reasonableness of the sentence. Id. at 569, 572.
At resentencing the district court sentenced both Sardin and St. Julian to seventy-two months imprisonment. This time the district court explained its methodology in arriving at the sentences as follows:
To arrive at the appropriate sentence, a hypothetical guideline will be used in-order to properly place the Defendant within an acceptable range.
The base offense level, based on thirty-six ounces, would be thirty-six.
.... [after additions and subtractions for other factors]
This results in a total offense level of thirty-nine.
Based on a total offense level of thirty-nine and a criminal history of one, the hypothetical guideline range is two hundred and sixty-two months to three hundred and twenty-seven months.
The Court finds that an upward departure to this degree is not warranted.
The seventy-two month sentence imposed, after careful consideration of the Defendant’s age and short duration of the conspiracy, the fact there is no history of drug abuse and the Defendant’s cooperation, I find that this is an appropriate sentence.
II Sardin R. 9-10; see also II St. Julian R. 9-10 (same methodology resulting in hypothetical offense level of 38 with criminal history category of II and suggested sentence of 262 to 327 months). The district court also explained the difference between their sentences and codefendant Davis’ lower sentence. Using the same hypothetical base offense level, Davis’ hypothetical sentencing range would have been from 151 to 188 months. II Sardin R. 10; II St. Julian R. 10-11.
II
Under the test we have heretofore applied, we will approve a sentencing that is an upward departure from the sentencing guidelines range if (1) the district court cited appropriate circumstances warranting departure from the guidelines; (2) the evidence supports the alleged justification for departing from the guidelines; and (3) the degree of departure is reasonable. White, 893 F.2d 276, 277-78 (10th Cir.1990). Only the third prong of the White test, the reasonableness of the degree of departure, is at issue in these appeals. To facilitate review of the reasonableness of the sentence, we have required that a district court explain the degree of departure, Jackson, 921 F.2d at 990 (citing 18 U.S.C. § 3553(c)), and held that the required reasons for the degree of departure are not synonymous with the reasons for departure. See United States v. Kalady, 941 F.2d 1090, 1100 (10th Cir.1991) (“Explanation of why a departure is made cannot fulfill this separate requirement” of explaining the degree of departure.).
After the instant appeals were submitted, the Supreme Court decided Williams v. United States, - U.S.-, 112 S.Ct. 1112, 117 L.Ed.2d 341 (1992). In Williams the Court was considering the appropriate standard of review when a district court relies upon both proper and improper grounds for a departure from the sentencing guidelines. In that context the Supreme Court suggested a two-part inquiry:
First, was the sentence imposed either in violation of law or as a result of an incorrect application of the Guidelines? If so, a remand is required under [18 U.S.C.] § 3742(f)(1). If the court concludes that the departure is not the result of an error in interpreting the Guidelines, it should proceed to the second step: is the resulting sentence an unreasonably high or low departure from the relevant guideline range? If so, a remand is required under [18 U.S.C.] § 3742(f)(2).
112 S.Ct. at 1120.
Although it is a different formulation, we do not believe Williams affects the analytical framework we have utilized, except as to when we remand for resentenc-ing when the district court erred, an issue discussed hereafter. Because we must review any upward departure from the guidelines for reasonableness, we continue to need information on the thought processes of the district court, as set out in Jackson. The focus of the appeals before us is on the reasonableness of the district court’s departures.
One of the chief objectives of the sentencing guidelines was to have “reasonable uniformity in sentencing by narrowing the wide disparity in sentences imposed for similar criminal offenses committed by similar offenders.” U.S.S.G. Ch. 1, Pt. A, intro. (n. 3), p.s.; see also Jackson, 921 F.2d at 988. To effectuate this purpose, we have required reference to the guidelines in determining the appropriate degree of departure. See St. Julian, 922 F.2d at 569 (“The guidelines are not discarded” after deciding to depart from the guidelines.); United States v. Roth, 934 F.2d 248, 252 (10th Cir.1991) (“reasons must be couched in terms of inadequacies in an offense level or criminal history category”). In St. Julian we suggested the appropriate method the district court should follow in formulating sentences outside the guidelines. After finding that the amount of drugs in this case “demands an adjustment in the offense level,” St. Julian, 922 F.2d at 569, we stated:
The next step is to turn to the guidelines and determine the most appropriate offense level.
This step is directly analogous to the prescribed method for calculating degree of departure based on criminal history. See U.S.S.G. § 4A1.3, p.s. In that situation, the appropriate criminal history category is selected using “as a reference, the guideline range for a defendant with a higher or lower criminal history category, as applicable.” Id._ In the case of offense level departures, the court must look to the offense level specified for a defendant whose offense conduct most closely resembles that of the defendant being sentenced.
Id.; see also Jackson, 921 F.2d at 991 (“a court may ‘treat the aggravating factor as a separate crime and ask how the defendant would be treated if convicted of it.’ ” (quoting United States v. Ferra, 900 F.2d 1057, 1062 (7th Cir.1990))).
A review of the record of the resentenc-ing hearing reveals that the district court did exactly as directed in our St. Julian opinion and as suggested by our en banc court in Jackson. The court treated the aggravating factor of the amount of drugs — thirty-six ounces of cocaine base— as a separate crime and calculated a hypothetical offense level with the following results:
See II St. Julian R. 8-11; II Sardin R. 8-10; 21 U.S.C. § 856(b); see also U.S.S.G. § 2Dl.l(c)(4); id. Ch. 5, Pt.A, sentencing table.
The district court then found that sentences in the hypothetical sentencing range would be inappropriately high for Sardin and St. Julian for two reasons: (1) the hypothetical range exceeded the twenty year statutory maximum for the crime of conviction, see 21 U.S.C. § 856(b); and (2) the factors in 18 U.S.C. § 3553: the nature and circumstances of the offense; the characteristics of the defendants, including their ages; the short duration of the conspiracy; the lack of history of drug abuse; and, in Sardin’s case, his cooperation.- II St. Julian R. 10; II Sardin R. 10.
The district court necessarily retains a great deal of discretion in imposing a sentence that departs upward from the guidelines. White, 893 F.2d at 278 (“Congress still envisioned that the Guidelines would leave considerable discretion in the hands of the sentencing judge”); id. at 279 (citing U.S.S.G. § 5K2.0, p.s.); see also Williams, 112 S.Ct. at 1121 (district courts retain sentencing discretion); United States v. Ocasio, 914 F.2d 330, 336 (1st Cir.1990) (“trial judge is in the trenches and is apt to be best informed about the offense and the offender” and “neither Congress nor the Commission contemplated doing away completely with individualized sentencing”). “The district court does have discretion in this area, of course, and need only give a reasonable methodology hitched to the Sentencing Guidelines to justify the reasonableness of the departure.” United States v. Harris, 907 F.2d 121, 123-24 (10th Cir. 1990).
After finding an appropriate hypothetical sentencing guidelines range and considering it, the district court was within its discretion in departing downward from the hypothetical range in light of both the statutory maximum and the factors articulated by the court In the area of upward departures there are no magic formulas that a court may apply automatically to calculate a proper sentence. In cases similar to those now before us, either the top of the hypothetical sentencing range or the statutory maximum, whichever is lower, establishes the upper limit to the court’s sentencing discretion. See Jackson, 921 F.2d at 991 (“the district court cannot impose a sentence exceeding the sentence the defendant would have received had she been convicted on the basis of the acts that warrant a departure”). The court then should consider, in light of the factors in 18 U.S.C. § 3553, if a sentence in that range is reasonable. See Davis, 922 F.2d at 617-18 (balancing aggravating and mitigating circumstances to arrive at appropriate departure is proper); see also United States v. Lira-Barraza, 941 F.2d 745, 751 (9th Cir. 1991) (en banc) (“a reasonableness standard assumes a range of permissible sentences”).
The district court did not state precisely why it chose seventy-two months instead of some other total between the top of the applicable guidelines range for the underlying offense and what was permissible for its hypothetical crime of distribution of thirty-six ounces of cocaine base. But we believe the Supreme Court in Williams clarified our role in this situation. If we conclude “that the departure is not the result of an error in interpreting the Guidelines, [we] should proceed to the second step: is the resulting sentence an unreasonably high or low departure....” Williams, 112 S.Ct. at 1120. District court error does not require remand if the departure is reasonable and we are convinced the district court “would have imposed the same sentence absent the erroneous factor.” Id. at 1121; see also id. at 1128 (White, J., dissenting) (“In light of the surviving reasons enunciated by the district court, the appellate court must determine for itself the ‘reasonableness’ of the departure under the factors to be considered when imposing sentence.”). We conclude that the degree of upward departure by the district court in defendants’ resentencing was reasonable and that if we were to remand again for more articulation of its reasoning the district court would give the same sentences.
III
The court must still consider whether the difference between defendants’ sentences and codefendant Davis’ sentence violated our direction in Sardin that “[g]iven that the three defendants here were ‘similar offenders’ engaged in ‘similar criminal conduct’ with respect to the reason given for their upward departure, they should have received equivalent upward departures.” Sardin, 921 F.2d at 1067.
Sardin now enjoys a sentence equal to St. Julian’s sentence instead of the four year disparity of the original sentences. The difference in defendants’ original sentences was striking because both defendants had the same sentencing guidelines range and the same rationale for departure. Davis, however, never was similarly situated because his offense level and criminal history category resulted in a significantly lower guidelines range. Moreover, the district court recognized other mitigating factors including Davis’ “very young age, problems resulting from peer pressure decisions, and [his] continuous involvement in mental health counseling over a protracted period.” Davis, 922 F.2d at 617.
We cannot accept defendants’ arguments that they are entitled to a cap on the amount their sentences could be enhanced corresponding with the exact number of months Davis’ sentence was enhanced. The district court applied our direction in St. Julian and Jackson and found hypothetical sentencing ranges for all three co-defendants. These ranges differed significantly for Davis and defendants based on Davis’ lower offense level and criminal history category of I. As the district court noted, the difference between the maximum possible sentence under Davis’ hypothetical guidelines range and defendants’ minimum possible sentence under defendants’ hypothetical guidelines range was seventy-four months. Differences in sentences due to differing offense levels and criminal history categories become more pronounced in terms of actual months in the higher offense levels. Considering Davis’ unique circumstances, Davis and defendants were treated m roughly the same way.
It appears that the sentences imposed on all three defendants are roughly equivalent in another sense. Davis’ actual sentence is a seventy-six percent downward departure from his minimum hypothetical sentencing range, while defendants’ actual sentences are seventy-three percent below their minimum hypothetical sentencing range. We do not require mathematical precision. United State v. Gardner, 905 F.2d 1432, 1438 (10th Cir.) (“formulas of mathematical exactitude are neither required nor permissible”), cert. denied, - U.S. -, 111 S.Ct. 202, 112 L.Ed.2d 163 (1990).
To the extent that Sardin’s, St. Julian’s, and Davis’ situations were equivalent, all three received “equivalent upward departures.” Sardin, 921 F.2d at 1067. Thus, the district court complied with our mandate.
AFFIRMED.
. After examining the briefs and appellate record, this panel has determined unanimously that oral argument in No. 91-6065 would not materially assist the determination of this appeal. See Fed.R.App.P. 34(a); 10th Cir.R. 34.1.9. This case is therefore ordered submitted without oral argument.
. St. Julian also suggests that whether the district court failed to consider his cooperation is an issue on appeal. That issue is not discussed anywhere in the brief. Counsel did argue before the district court at sentencing that cooperation was a justification for limiting the upward departure. On this sparse record, however, we cannot review the issue. Moreover, as is apparent from our analysis of the issues discussed in this opinion, we doubt that we could find an abuse of discretion had the issue been raised satisfactorily.
.The sentences also include terms of supervised release, not important to the determination of this appeal.
. Apparently, the separate crime the court considered was distribution of the thirty-six ounces of cocaine base. See Davis, 922 F.2d at 617.