Editing ABA routing transit number (section)

==Formats==
[[File:Knuth-check2.png|300px|thumb|right|A check showing the fraction form (top middle-right, ''11-3167/1210'' plus branch number 01) and MICR form (bottom left, ''129131673'') of the transit number.]]
The ABA RTN appears in two forms on a standard check – the fraction form and the [[MICR]] (magnetic ink character recognition) form.<ref name="bo04" /> Both forms give essentially the same information, though there are slight differences.

The MICR forms are the main form&nbsp;– it is printed in magnetic ink, and is machine-readable; it appears at the bottom left of a check, and consists of nine digits.

The fraction form was used for manual processing before the invention of the MICR line, and still serves as a backup in check processing should the MICR line become illegible or torn; it generally appears in the upper right part of a check near the date.

The MICR number is of the form
: XXXXYYYYC
where XXXX is Federal Reserve Routing Symbol, YYYY is ABA Institution Identifier,
and C is the Check Digit, while the fraction is of the form:
: PP-YYYY/XXXX
where PP is a 1 or 2 digit Prefix, no longer used in processing, but still printed, representing the bank's check processing center location, with 1 through 49 for processing centers located in a major city, and 50 through 99 representing processing is done at a non-major city in a particular state. Sometimes a branch number or the account number are printed below the fraction form; branch number is not used in processing, while the account number is listed in MICR form at the bottom. Further, the Federal Reserve Routing Symbol and ABA Institution Identifier may have fewer than 4 digits in the fraction form. The essential data, shared by both forms, is the Federal Reserve Routing Symbol (XXXX), and the ABA Institution Identifier (YYYY), and these are usually the same in both the fraction form and the MICR, with only the order and format switched (and left-padded with 0s to ensure that they are 4 digits long).

The prefix and the Federal Reserve Routing Symbol (XXXX) are determined by the bank's geographical location and treatment by the Federal Reserve type, while the remaining data (YYYY, and Branch number, if present) depends on the specific bank, and are unique within a Federal Reserve district.

In the check depicted above right, the fraction form is ''11-3167/1210'' (with ''01'' below it) and MICR form is ''129131673'' which are analyzed as follows:
* the ''prefix'' 11 corresponds to San Francisco,
* 3167 (common to both) is the ABA Institution Identifier,
* 1210 and 1291 are the Federal Reserve Routing Symbols (generally equal, here different probably due to obfuscation, see image file history for more information), with the initial "12" corresponding to the Federal Reserve Bank of San Francisco, the third digits ("1" and "9") corresponding to check processing centers, and the fourth digits ("0" and "1") corresponding to where the bank is located&nbsp;– "0" indicates "in the Federal Reserve city of San Francisco", while "1" indicates "in the state of California".
* the final "3" in the MICR is the check digit, and
* the "01" below the fraction form is the branch number.

In the case of a MICR line that is illegible or torn, the check can still be processed without the check digit. Typically, a repair strip or sleeve is attached to the check, then a new MICR line is imprinted. Either 021200025 or 0212-0002 (with a hyphen, but no check digit) may be printed, and both are 9 digits. The former (with check digit) is preferred to ensure better accuracy, but requires computing the check digit, while the latter is easily determined by inspection of the fraction, with minimal clerical handling.

===MICR routing number format===
The MICR routing number consists of nine digits:
: XXXXYYYYC
where XXXX is Federal Reserve Routing Symbol, YYYY is ABA Institution Identifier,
and C is the check digit.

====Federal Reserve====
The Federal Reserve uses the ABA RTN system for processing its customers' payments.  The ABA RTNs were originally assigned in the systematic way outlined below, reflecting a financial institution's geographical location and internal handling by the Federal Reserve. Following consolidation of the Federal Reserve's check processing facilities, and the consolidation in the banking industry, the RTN a financial institution uses may not reflect the "Fed District" where the financial institution's place of business is located.  Check processing is now centralized at the Federal Reserve Bank of Atlanta.<ref name="bur05">{{Harv|Burnett|2005}}</ref>

The first two digits of the nine digit RTN must be in the ranges 00 through 12, 21 through 32, 61 through 72, or 80.

The digits are assigned as follows:
* 00 is used by the [[Federal government of the United States|United States Government]]
* 01 through 12 are the "normal" routing numbers, and correspond to the 12 [[Federal Reserve Bank]]s. For example, 0260-0959-3 is the routing number for Bank of America incoming wires in New York, with the initial "02" indicating the [[Federal Reserve Bank of New York]].
* 21 through 32 were assigned only to [[Cooperative banking|thrift institutions]] (e.g. [[credit union]]s and savings banks) through 1985, but are no longer assigned (thrifts are assigned normal 01–12 numbers). Currently they are still used by the thrift institutions, or their successors, and correspond to the normal routing number, plus 20. (For example, 2260-7352-3 is the routing number for Grand Adirondack Federal Credit Union in New York, with the initial "22" corresponding to "02" (New York Fed) plus "20" (thrift).)
* 61 through 72 are special purpose routing numbers designated for use by non-bank payment processors and clearinghouses and are termed Electronic Transaction Identifiers (ETIs), and correspond to the normal routing number, plus 60.
* 80 is used for [[traveler's check]]s

The first two digits correspond to the 12 [[Federal Reserve Bank]]s as follows:

{| class="wikitable"
! Primary<br />(01–12)
! Thrift<br/>(+20)
! Electronic<br/>(+60)
! Federal Reserve Bank
|-
|01 || 21 || 61 || [[Federal Reserve Bank of Boston|Boston]]
|-
|02 || 22 || 62 || [[Federal Reserve Bank of New York|New York]]
|-
|03 || 23 || 63 || [[Federal Reserve Bank of Philadelphia|Philadelphia]]
|-
|04 || 24 || 64 || [[Federal Reserve Bank of Cleveland|Cleveland]]
|-
|05 || 25 || 65 || [[Federal Reserve Bank of Richmond|Richmond]]
|-
|06 || 26 || 66 || [[Federal Reserve Bank of Atlanta|Atlanta]]
|-
|07 || 27 || 67 || [[Federal Reserve Bank of Chicago|Chicago]]
|-
|08 || 28 || 68 || [[Federal Reserve Bank of St. Louis|St. Louis]]
|-
|09 || 29 || 69 || [[Federal Reserve Bank of Minneapolis|Minneapolis]]
|-
|10 || 30 || 70 || [[Federal Reserve Bank of Kansas City|Kansas City]]
|-
|11 || 31 || 71 || [[Federal Reserve Bank of Dallas|Dallas]]
|-
|12 || 32 || 72 || [[Federal Reserve Bank of San Francisco|San Francisco]]
|}

The third digit corresponds to the Federal Reserve check processing center originally assigned to the bank.<ref name="bur05" />

The fourth digit is "0" if the bank is located in the Federal Reserve city proper, and otherwise is 1–9, according to which state in the Federal Reserve district it is.<ref name="bur05" />

====ABA Institution Identifier====
The fifth through eighth digits constitute the bank's unique ABA identity within the given Federal Reserve district.<ref name="bur05" />

====Check digit====
The ninth, [[check digit]] provides a [[checksum]] test using a position-weighted sum of each of the digits. High-speed check-sorting equipment will typically verify the checksum and if it fails, route the item to a reject pocket for manual examination, repair, and re-sorting. Mis-routings to an incorrect bank are thus greatly reduced.

The following condition must hold:<ref name="bo04" />

:{{math|1=(3({{var|d}}{{sub|1}} + {{var|d}}{{sub|4}} + {{var|d}}{{sub|7}}) + 7({{var|d}}{{sub|2}} + {{var|d}}{{sub|5}} + {{var|d}}{{sub|8}}) + ({{var|d}}{{sub|3}} + {{var|d}}{{sub|6}} + {{var|d}}{{sub|9}})) mod 10 = 0}}

: ([[Modulo operation|Mod]] or modulo is the remainder of a division operation.)
In terms of weights, this is 371 371 371. This allows one to catch any single-digit error (incorrectly inputting one digit), together with most transposition errors. 1, 3, and 7 are used because they (together with 9) are [[coprime]] to 10; using a coefficient that is divisible by 2 or 5 would lose information (because <math>5 \cdot 0 = 5 \cdot 2 = 5 \cdot 4 = 5 \cdot 6 = 5 \cdot 8 = 0 \mod 10</math>), and thus would not catch some substitution errors. These do not catch transpositions of two digits that differ by 5 (0 and 5, 1 and 6, 2 and 7, 3 and 8, 4 and 9), but captures other transposition errors.{{citation needed|date=April 2013}}

As an example, consider 111000025 (which is a valid routing number of [[Bank of America]] in [[Virginia]]). Applying the formula, we get:

: {{math|1= (3(1&thinsp;+&thinsp;0&thinsp;+&thinsp;0) + 7(1&thinsp;+&thinsp;0&thinsp;+&thinsp;2) + (1&thinsp;+&thinsp;0&thinsp;+&thinsp;5)) mod 10 = 0}}.

====Routing symbol====
[[File:OCR branch bank identification.svg|50px|right]]

The symbol that delimits a routing transit number is the [[MICR]] [[E-13B]] transit character ⑆ This character, with Unicode value U+2446, appears at right.

===Fraction format===
The fraction form looks like a [[fraction (mathematics)|fraction]], with a [[numerator]] and a [[denominator]].

The numerator consists of two parts separated by a dash. The prefix (no longer used in check processing, yet still printed on most checks) is a 1 or 2 digit code (P or PP) indicating the region where the bank is located. The numbers 1 to 49 are cities, assigned by size of the cities in 1910. The numbers 50 to 99 are states, assigned in a rough spatial geographic order, and are used for banks located outside one of the 49 numbered cities.

The second part of the numerator (after the dash) is the bank's ABA Institution Identifier, which also forms digits 5 to 8 of the nine digit routing number (YYYY).

The denominator is also part of the routing number; by adding leading zeroes to make up four digits where necessary (e.g. 212 is written as 0212, 31 is written as 0031, etc.), it forms the first four digits of the routing number (XXXX).

There might also be a fourth element printed to the right of the fraction: this is the bank's branch number. It is not included in the MICR line. It would only be used internally by the bank, e.g. to show where the signature card is located, where to contact the responsible officer in case of an overdraft, etc.

For example, a check from Wachovia Bank in Yardley, PA, has a fraction of 55-2/212 and a routing number of 021200025. The prefix (55) no longer has any relevance, but from the remainder of the fraction, the first 8 digits of the routing number (02120002) can be determined, and the check digit (the last digit, 5 in this example) can be calculated by using the [[#Internal checksums|check digit formula]] (thus giving 021200025).

====ABA prefix table====
This table is up to date as of 2020. One weakness of the current routing table arrangement is that various territories like American Samoa, Guam, Puerto Rico and the US Virgin Islands share the same routing code.

{| class="wikitable"
|-
! Prefix
! Location
|-
| 1
| New York, NY
|-
| 2
| Chicago, IL
|-
| 3
| Philadelphia, PA
|-
| 4
| St. Louis, MO
|-
| 5
| Boston, MA
|-
| 6
| Cleveland, OH
|-
| 7
| Baltimore, MD
|-
| 8
| Pittsburgh, PA
|-
| 9
| Detroit, MI
|-
| 10
| Buffalo, NY
|-
| 11
| San Francisco, CA
|-
| 12
| Milwaukee, WI
|-
| 13
| Cincinnati, OH
|-
| 14
| New Orleans, LA
|-
| 15
| Washington D.C.
|-
| 16
| Los Angeles, CA
|-
| 17
|  Minneapolis, MN
|-
| 18
| Kansas City, MO
|-
| 19
| Seattle, WA
|-
| 20
| Indianapolis, IN
|-
| 21
| Louisville, KY
|-
| 22
| St. Paul, MN
|-
| 23
| Denver, CO
|-
| 24
| Portland, OR
|-
| 25
| Columbus, OH
|-
| 26
| Memphis, TN
|-
| 27
| Omaha, NE
|-
| 28
| Spokane, WA
|-
| 29
| Albany, NY
|-
| 30
| San Antonio, TX
|-
| 31
| Salt Lake City, UT
|-
| 32
| Dallas, TX
|-
| 33
| Des Moines, IA
|-
| 34
| Tacoma, WA
|-
| 35
| Houston, TX
|-
| 36
| St. Joseph, MO
|-
| 37
| Fort Worth, TX
|-
| 38
| Savannah, GA
|-
| 39
| Oklahoma City, OK
|-
| 40
| Wichita, KS
|-
| 41
| Sioux City, IA
|-
| 42
| Pueblo, CO
|-
| 43
| Lincoln, NE
|-
| 44
| Topeka, KS
|-
| 45
| Dubuque, IA
|-
| 46
| Galveston, TX
|-
| 47
| Cedar Rapids, IA
|-
| 48
| Waco, TX
|-
| 49
| Muskogee, OK
|-
| 50
| New York
|-
| 51
| Connecticut
|-
| 52
| Maine
|-
| 53
| Massachusetts
|-
| 54
| New Hampshire
|-
| 55
| New Jersey
|-
| 56
| Ohio
|-
| 57
| Rhode Island
|-
| 58
| Vermont
|-
| 59
| Hawaii
|-
| 60
| Pennsylvania
|-
| 61
| Alabama
|-
| 62
| Delaware
|-
| 63
| Florida
|-
| 64
| Georgia
|-
| 65
| Maryland
|-
| 66
| North Carolina
|-
| 67
| South Carolina
|-
| 68
| Virginia
|-
| 69
| West Virginia
|-
| 70
| Illinois
|-
| 71
| Indiana
|-
| 72
| Iowa
|-
| 73
| Kentucky
|-
| 74
| Michigan
|-
| 75
| Minnesota
|-
| 76
| Nebraska
|-
| 77
| North Dakota
|-
| 78
| South Dakota
|-
| 79
| Wisconsin
|-
| 80
| Missouri
|-
| 81
| Arkansas
|-
| 82
| Colorado
|-
| 83
| Kansas
|-
| 84
| Louisiana
|-
| 85
| Mississippi
|-
| 86
| Oklahoma
|-
| 87
| Tennessee
|-
| 88
| Texas
|-
| 89
| Alaska
|-
| 90
| California
|-
| 91
| Arizona
|-
| 92
| Idaho
|-
| 93
| Montana
|-
| 94
| Nevada
|-
| 95
| New Mexico
|-
| 96
| Oregon
|-
| 97
| Utah
|-
| 98
| Washington
|-
| 99
| Wyoming
|-
|101
|American Samoa, Guam, Puerto Rico, Virgin Islands
|}