Factory shipments rose 5 per cent in March for the biggest gain in more than six years, the Commerce Department said yesterday.

Commerce also said factory orders gained 5.2 per cent for the second largest monthly increase since December 1970.

Shipments moved so quickly in March, the department said, that they matched orders for the auto industry. This meant there was no inventory building in the nation's most important production industry, at least at a seasonally adjusted rate.

The report was another sign of the economic recovery that President Carter said would continue without a federal stimulus from a $50 tax rebate for individuals and $4 billion in business incentives.

Commerce said shipments rose $5.3 billion to $111.4 billion in March. The 5 per cent increase was the biggest since a 5 per cent increase in December 1970.

New orders rose $5.6 billion to $112.1 billion. Commerce noted the 5.2 per cent advance was exceeded only once in the past 75 months - the 5.8 per cent rise last December.

Both shipments and orders were spurred by factories starting up again after the temporary closings caused by extreme cold weather in the Mid-west, East and South during January and early February. January orders and shipments declined, then in February advanced slightly when thee weate rhased late in the month.

New orders for durables increased 8 per cent in March. The $4.4 billion gain to $59.6 billion was led by a 20 per cent surge in transportation equipment. New orders for nondurables grew a modest 2 per cent.