A publisher packs 928 novels and 1160 workbooks into cartons. Every carton must hold books of only one kind, and all cartons must hold the same number of books.
What is the greatest number of books a carton can hold?

The carton size must divide both totals, so the greatest is HCF(928, 1160). Now $928=2^5\times$ 29 and $1160=2^3\times 5\times 29$, so HCF = $2^3\times$ 29 = 232 (4 cartons of novels and 5 of workbooks). Answering 116 gives a common factor that is not the greatest; 9 is the number of cartons, not the carton size; 464 does not divide 1160.