Tulip bulbs have divided

in Plants
Hello. I’ve decided to lift my tulips (first time doing this) and store them over summer in the hope of getting a good display from them next summer. I deadheaded after they flowered and have fed them. I waited until tonight when they were yellow and dry to lift the bulbs. However it seems like quite a few of the bulbs have divided and as a result are quite small. Will it be ok to replant these in autumn or has something gone wrong? I can’t be bothered to dry them out, store and replant if they are not going to make it! Should I just bother with the big ones? Thanks!
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Again some varieties seem to split more than others. I store all sizes of the potted bulbs and replant in November at that point I plant the largest ones first and pop small ones in between. Really tiny ones I scrap although I'm always sad to do it!