By pulling or cutting apart a large plant that has numerous shoots or buds growing together, any number of rooted sections can be obtained for separate potting. This is by far the quickest and easiest method of propagation. A large multiple-crowned African-violet readily produces a dozen or more new plants this way. Heleniums and chrysanthemums can be increased by the same means.
Plants that grow from a single stem or crown cannot be propagated this way, of course.
Clumps of dahlia tubers can be cut into sizable divisions each with a bit of top growth; hardy bulbs, gladiolus and cyclamen corms can be cut in half. But wherever you have to use a knife, be sure it is sterile. Take care to dust all cut surfaces of a plant with sulfur or a fungicide like Fermate to prevent the entrance of disease.
Lift a complete plant from its pot or from the ground but only when the plant is dormant and cut sections of the larger, more fleshy roots into 2- to 3-inch-long pieces. Cut the end of the root nearest the crown of the plant (that would be the top of the root) straight across, and cut the other end on a slant, so you can distinguish top from bottom and won't plant the cuttings upside down. Insert the root cuttings in pots or flats of rooting medium with the straight cut at the surface level of the medium.
The cuttings will develop roots, and growing points or crowns will form at the top ends of the cuttings.