Three logs of timber measuring 42 m, 49 m and 63 m are to be sawn into planks that are all the same whole number of metres long, with no wood left over. What is the greatest possible length of one plank?

The plank length must divide all three logs exactly, so it is the HCF. Factorising, $42=2\times 3\times 7,49=7\times 7$ and $63=3\times 3\times 7$, and the only prime shared by all three is 7. So the greatest length is 7 m, giving 6, 7 and 9 planks. Answering 21 uses only 42 and 63 and forgets the 49; answering 14 forgets the 63.