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In sequencing DNA, technicians break up long molecules into smaller pieces because it is easier to sequence small segments than long ones. They must then reconstruct the target molecule by fitting the small segments together using overlaps as a guide. The small segments are sequenced beginning at either end in a random fashion. So, for example, the segment ATACAG may also be sequenced as GACATA. In this puzzle, I have chopped up many identical 50-long sequences into pieces of lengths 5, 6, 7, and 8. 30 of these pieces are: ATACAG TGACAT GTCTTA GTCGAGA AACGA CAAGG CAGTGTGA GTGGTGT CCGATGAC AGACAA TGTGA ATACAGTG CTGTG ACATA GTGTCG TACAGT GTCTTAG CATAA GGTGG GACTCCAG TGTGA CCAGTG TGTGACA GTGACATA TGTGGT ATTCTGA TGAATACA TAGCCG TGTGACCT CCTCA I have insured that these 30 pieces completely cover the 50-long sequence with which I started. Can you find that sequence?

Yes.

common factor of difference between pairs of numbers