Your Remington 1903-A3 was made by Remington in 1942.
With the serial number that you have supplied,your Remington model 1903 rifle was made in the year 1941.
The original Remington was made in 1903 October 1943.
1941
October 1942.
It would be june of 1942
A chart/pdf of the 1903/1903a serial codes is post on the Remington Society of America. http://remingtonsociety.com/rsa/questions/barrelcodes
Without more information - range of value from 300-900.
Depending on condition 300-700
Your Remington model 1903-A3 was made in the year 1942.It was chambered in the caliber 30-06.
Your springfield model 1903 was made by springfield amory in 1918.The serial number you provided does not correspond with the other 2 makers of springfield rifles,rock island and remington.
your serial number 33486 is to low for the 1903a3 serial number range. however, the Remington model of 1917, serial number 33486 was made in 1918............. The 1903a3 and the model of 1918 both fire the 30/06 cartridge.................