A financial institution (FI) number is the 3-digit number that identifies your financial institution. These numbers are used today to identify a financial institution when processing a cheque, performing a bank trasfer or any other electronic payment.
Current financial institution numbers are:
Bank of Montreal - 001
Bank of Nova Scotia - 002
Royal Bank - 003
TD Canada Trust - 004
National Bank of Canada - 006
CIBC - 010
Here is how the number appears on a Canadian cheque.
It is encoded along the bottom of a cheque in a special font called MICR E-13B using magnetic ink.
The first 3 digits are the cheque number, followed by a 5 digit transit number (identifying the specific bank branch), then comes a 3 digit institution number (identifying the bank) and finally your account number.
Financial institution numbers came into being by Bank Act that eliminated hand countersignatures on banknotes and mandated a corporate logo and identifying number be imprinted on the banknote at the same time as the signatures. Institution numbers were assigned by "seniority" or in the order that the banks of the time received their charter. Thus the Bank of Montreal, Canada's oldest bank has number 001, or as it appeared on early banknotes, a "Saltire over 1". Here are some logos / bank numbers as they appear on chartered banknotes:
Bank of Montreal; Saltire
over 1.
Bank of Nova Scotia; Heraldic Lion in Shield above 2.
Bank of Toronto; BT
Monogram in Shield above 3.
Banque Canadienne Nationale; Beaver over 6
Royal Bank; Crown above 11.
On earlier banknotes this was enclosed in a circle. The circle was
omitted on the later notes.
Dominion Bank; Maple
Leaf above 12.
Imperial Bank; Saltire in
Circle over 17 or 
Heraldic Lion
in Circle over 17.
Barclays Bank; Eagle in
Shield below 22.
Other bank numbers found on chartered banknotes but not shown here are:
Molsons Bank; Arms over 3.
Merchants Bank; Sheaf over 7.
Banque Provinciale du Canada; Beaver on Maple Leaf to the left of 8.
Union Bank; Anchor in Circle over 9.
Canadian Bank of Commerce; Caduceus below 10.
La Banque Nationale; Maple Leaf over 10.
Bank of Hamilton; Beehive over 13.
Standard Bank; Heraldic Lion and Standard over 14.
Banque d'Hochelaga; Beaver over 15.
When the La Banque Nationale and the Banque d'Hochelaga merged the
logos also merged forming the Beaver and Maple Leaf of Banque
Canadienne Nationale.
The bank numbers also found their way onto bank cheques. Note the 14
above 315 within triangle on this Standard Bank cheque. The 14
identifies the Standard
Bank and the 315 identifies the Caledonia, Ontario branch. The 315 is
essentially a
"transit number". Note the Heraldic Lion on the left of the cheque
which is identical to that of the logo used on Standard Bank banknotes.
On November 1. 1979, the Provincial Bank of Canada (008), the Unity
Bank of Canada (018),
and the Bank Canadian National, merged to form the National Bank of
Canada (006). Institution
Numbers 008 and 018 were gradually replaced by 006