Beyond the Bible- The Census from the view of scholars

(The following is direct quotation from the Commentary of St. Jerome)
Critical scholars are unanimous in viewing the numbers given in this list as impossibly high and have proposed a number of theories to account for them.
(1) Albright suggested that we have a record of a census taken at a later period, specifically, a variant of the census taken by David according to 2 Samuel 24:1-9. However, the numbers seem too high even for the time of David.

(2) Others take the total figure of 603,550 as an example of gematria, i.e., play on the numberical value of the letters in certain words: the consonants in ‘bny ysr’l’, “sons of Israel”, add up to 603, and those in ‘kl r’ṧ’, “every head” add up to 550 if the quiescent aleph in r’ṧ is ignored. However, there is no evidence that the letters of the alphabet had these numberical values during the period in which the Priestly authors worked.

(3) G Mendenhall built upon the fact that the Hebrew word for “thousand,” `elep sometimes refers to a subdivision within a tribe (e.g., Judges 6:15 and Micah 5:1). If the same word in our passage were taken to mean something like “contingent,” then the total given for Reuben, e.g., could be read as “46 contingents with a total of 500 men,” instead of “46,500 men.” This approach leads to results that are difficult to explain, for on its reckoning, the contingents from the tribe of Gad averaged 14 men while those from Simeon had only 5! In any case, the total given in v 46 requires that the word `elep be taken in its numerical sense.

(4) Budd points to the fact that the Priestly writers were aware of older Yahwistic traditions which gave a round number of 600,000, presumably for the total population of the exodus generation. On the other hand, the Priestly calculation of the amount of silver required for the bases and hooks of the tabernacle came to 301,775 shekels. Uisng the postexilic rate of one-half shekel tax for each adult male leads to the figure 603,550. Having reached this total, the priests would have distributed the number among the twelve tribes in proportions that seemed plausible to them.