This paper presents a test resource partitioning technique based on an efficient response compaction design called quotient compactor(q-Compactor). Because q-Compactor is a single-output compactor, high compaction ratios can be obtained even for chips with a small number of outputs. Some theorems for the design of q-Compactor are presented to achieve full diagnostic ability, minimize error cancellation and handle unknown bits in the outputs of the circuit under test (CUT). The q-Compactor can also be moved to the load-board, so as to compact the output response of the CUT even during functional testing. Therefore, the number of tester channels required to test the chip is significantly reduced. The experimental results on the ISCAS ’89 benchmark circuits and an MPEG 2 decoder SoC show that the proposed compaction scheme is very efficient.