The German cockroach is the most common species of cockroach. German cockroaches can breed at a rate of up to six generations per year. The German cockroach can fit through an opening as small as 3/8 inch in width. German cockroaches will feed on almost anything, including soap, glue and toothpaste. German cockroaches are good hitchhikers and often find their way into new structures via grocery bags, cardboard boxes, drink cartons and secondhand appliances. German cockroaches prefer to live in warm, humid places close to food and moisture sources. They are frequently found in residential and commercial kitchen environments, and bathrooms.