Terrance Sykes appeals from his conviction of: (1) one count of possession with intent to distribute fifty grams or more of a mixture and substance containing a detectable amount of cocaine base in violation of 21 U.S.C. § 841(b)(1)(A); and (2) one count of simple possession of five or more grams of cocaine base in violation of 21 U.S.C. § 844(a). We assume the parties’ familiarity with the facts, the procedural history, and the issues on appeal.
In this appeal, Sykes challenges his conviction and sentence on three grounds: (1) the warrant pursuant to which law enforcement searched his residence and vehicle was not supported by probable cause; (2) the vehicle searched by law enforcement was not within the scope of the war*12rant; and (3) his sentence is unconstitutionally cruel and unusual.
Defendant’s principal argument is that the district court erred in failing to suppress on Fourth Amendment grounds evidence seized as a result of the searches of Defendant’s residence and vehicle. “With respect to a denial of the motion to suppress, we review the district court’s factual findings for clear error, and review its conclusions of law de novo.” United States v. Irving, 452 F.3d 110, 123 (2d Cir.2006).
Defendant first argues that the warrant to search his apartment and its curtilage was not supported by probable cause. A judicial officer issuing a warrant must “make a practical, common-sense decision whether, given all the circumstances set forth in the affidavit before him, ... there is a fair probability that contraband or evidence of a crime will be found in a particular place.” Illinois v. Gates, 462 U.S. 213, 238, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983). The probable cause determination here was based on the law enforcement officer’s observations and firsthand knowledge and on statements made by a known, reliable confidential informant, which were corroborated by law enforcement. The “totality-of-the-circumstanees” therefore supports issuance of the warrant. See id.; United States v. Gagnon, 373 F.3d 230, 235 (2d Cir.2004). Likewise, Defendant’s argument that we may not apply the good faith exception because the “affidavit is so lacking in indicia of probable cause as to render official belief in its existence entirely unreasonable” lacks merit. United States v. Singh, 390 F.3d 168, 181 (2d Cir.2004).
Plaintiff next challenges the search of his vehicle as beyond the scope of the warrant.1 Because we find that any error *13was harmless with respect to the search of Defendant’s vehicle, however, we need not reach the question of whether any constitutional violation occurred.
Where an error of constitutional dimension occurs, we must vacate a conviction unless we are “convinced that the error was harmless beyond a reasonable doubt.” United States v. Reifler, 446 F.3d 65, 87 (2d Cir.2006). As “we consider the nature of the violation and the context in which it occurred” to evaluate the error’s likely impact, several factors are relevant: (1) the strength of the Government’s case; (2) the degree to which the inadmissible evidence was material to a critical issue; (3) the extent to which the evidence was cumulative; and (4) the degree to which the Government emphasized the evidence in its presentation of its case. Id. Though all of these factors are relevant, we have stated that the strength of the Government’s case is “probably the single most critical factor.” Id. (internal quotation marks omitted).
The strength of the Government’s case against Sykes was overwhelming. Found in the bag beneath Sykes when he was arrested was enough cocaine alone to meet the threshold for possession with intent to distribute 50 grams or more of a substance containing cocaine base — notwithstanding the almost 700 grams of cocaine Sykes concedes were found elsewhere in the residence. See 21 U.S.C. § 841(a)(1), (b)(1)(A)(iii). The fact that Sykes was lying on top of the bag when the officers found him in the apartment would be sufficient for a jury to connect him to at least the 57.16 grams of cocaine Sykes concedes were found in that bag. As such, the evidence obtained from the vehicle was cumulative and not material to the establishment of a critical fact. Additionally, the evidence was not emphasized by the prosecutor in arguments to the jury, and the jury’s deliberations were speedy, indicating that they did not appear to regard the ease as a “close” one. See United States v. Dhinsa, 243 F.3d 635, 649-50 (2d Cir.2001).
We therefore conclude that it is not only “highly probable that the error did not contribute to the verdict,” United States v. Colombo, 909 F.2d 711, 713 (2d Cir.1990) (internal quotation marks omitted), but also “beyond a reasonable doubt that a rational jury would have rendered a verdict of guilty absent the alleged error.” Dhinsa, 243 F.3d at 649; see also United States v. Lombardozzi, 491 F.3d 61 (2d Cir.2007); Reifler, 446 F.3d at 87. As we “possess[ ] a sure conviction that the error did not prejudice the defendant,” any improper admission of evidence from Sykes’s vehicle was harmless. Dhinsa, 243 F.3d at 649.
Finally, Defendant argues that his sentence of life imprisonment is disproportionate to his crime and thus violates the Eighth Amendment as “cruel and unusual.” Defendant’s sentence does not implicate the Eighth Amendment, which “forbids only extreme sentences that are grossly disproportionate to the crime.” United States v. Yousef, 327 F.3d 56, 163 (2d Cir.2003) (internal quotation marks *14omitted). The Supreme Court has indicated that “three-strike” recidivist provisions requiring imposition of a life sentence upon commission of a third triggering offense—like § 841(b)(1)(A)—do not violate the Eighth Amendment. See Rummel v. Estelle, 445 U.S. 263, 100 S.Ct. 1133, 63 L.Ed.2d 382 (1980). Based on Defendant’s multiple felony drug convictions, the district court properly sentenced Defendant in accordance with the mandatory minimum sentence prescribed by 21 U.S.C. § 841(b)(1)(A). His challenge is without merit.
We have considered all of Sykes’s other arguments and find them to be without merit. For the reasons stated herein, we AFFIRM the judgment of the district court.
. The warrant authorized a search of "# 263 Emerson St., down ... described as a two story, multi-family dwelling,” and further specified that entry was to be made through a particular door leading "directly into the apartment.” The warrant also stated that the "areas to be searched [are] the entire premises described above, including all its storage areas and curtilage.” Relying on the language of the warrant, the district court found that the automobile search was proper because the warrant authorized a search of the “premises” and "its ... curtilage.”
We take this opportunity to note, as Judge Friendly did almost thirty years ago, "[terming a particular area curtilage expresses a conclusion; it does not advance Fourth Amendment analysis.” United States v. Arboleda, 633 F.2d 985, 992 (2d Cir.1980). Defining an area as curtilage is a legal conclusion that "relies essentially on factual determinations.” United States v. Reilly, 76 F.3d 1271, 1275 (2d Cir.1996). We base our definition of the curtilage of particular premises on "factors that bear upon whether an individual reasonably may expect that the area in question should be treated as the home itself,” with a special focus on "whether the area harbors the intimate activity associated with the sanctity of a man's home and the privacies of life.” United States v. Titemore, 437 F.3d 251, 258 (2d Cir.2006) (internal quotation marks omitted).
The factual determination of whether a vehicle is included within the scope of particular premises’ curtilage may vary depending on, inter alia, whether the premises host a single-family or a multi-family dwelling. Compare United States v. Freeman, 685 F.2d 942, 955 (5th Cir.1982) (search warrant for defendant's house justified search of vehicle “parked off the street and close to the house”) with Mack v. City of Abilene, 461 F.3d 547, 554 (5th Cir.2006) (finding apartment dweller’s parking space was not within the curtilage of his apartment). The curtilage analysis of a unit within a multi-family dwelling will also depend on the degree of privacy tenants of that particular multi-family dwelling can reasonably expect in a particular location on the premises. See e.g., United States v. Holland, 755 F.2d 253, 255 (2d Cir.1985) (”[T]he common halls and lobbies of multi-tenant buildings are not within an individual tenant’s zone of privacy even though they are guarded by locked doors.”); Fixel v. Wainwright, 492 *13F.2d 480, 484 (5th Cir.1974) (defendant could "reasonably expect privacy” in the backyard area of a multi-unit residence where the backyard was "sufficiently removed and private in character”).
In light of these considerations, we would require additional fact finding by the district court in order to determine whether Sykes had a reasonable expectation of privacy in the backyard area where the vehicle was located that would bring it within the scope of the curtilage of his apartment. Because we find that any improper admission of evidence found in the vehicle was harmless, however, neither we nor the district court need conduct that further Fourth Amendment analysis.