1926, since it's after 1920 it should also have the barrel code.
They month and year can be determined by the barrel code, all the details can be found on the Remington Society of America here:
http://remingtonsociety.com/rsa/questions/barrelcodes
Need the serial number to answer.
1919
1913
1931
1920
The Remington Model 740 was manufactured from 1955 to 1980. To determine the specific year of your firearm's manufacture, you can check the serial number, as Remington provides a date code based on this number. If you have the serial number, you can consult Remington's records or online resources for precise information.
You cannot the serial number is required.
The serial number 4279990 is a partial serial number for this rifle. To determine the date the rifle was manufactured you need to provide a complete serial number that begins with letters.
In 1944 by Remington Rand
1920
Manufactured 1916
Manufactured 1931