Three rolls of craft tape measure 105 cm, 175 cm and 210 cm. They are cut into equal pieces of the greatest possible length with nothing left over.
How many pieces are obtained altogether?

Each piece is HCF(105, 175, 210) long. $105=3\times 5\times 7,175=5^2\times$ 7 and $210=2\times 3\times 5\times 7$, so HCF = $5\times 7=35$ cm. The rolls then give 105/35 = 3, 175/35 = 5 and 210/35 = 6 pieces, a total of 14. Answering 35 gives the piece length instead of the number of pieces; 98 comes from using 5 cm as the HCF.