With franchise applications due in six weeks, Canada's Rogers Telecommunications Ltd., the largest cable television firm in North America, announced yesterday it is dropping out of contention for the Montgomery County cable franchise.

The Canadian firm formed a partnership last summer with the Tribune Co., the giant parent company of The Chicago Tribune and New York Daily News, to seek the Montgomery franchise. At that time Edward Rogers, vice chairman of Rogers Telecommunications, pledged to offer Montgomery residents "the most advanced system" on the continent.

The Rogers withdrawal came as Tribune officials announced that they had replaced the Canadian media company with United Cable Television Corp., a Denver firm that is the 12th largest cable-system operator in the United States.

United, which also is seeking the franchise award in Fairfax County, serves more than 430,000 subscribers in 84 communities, while Tribune serves about 100,000 subcribers and operates WGN-TV, the Chicago station that is carried by satellite to cable systems reaching more than 7 million homes. Tribune also owns a system in Gaithersburg.

In announcing its retrenchment, Rogers said it dropped out of the Montgomery competition as a result of a new corporate policy limiting its pursuit of franchises to areas "which are contiguous to existing franchises."