A rectangular plot measures 693 m by 462 m. Fence posts are to be fixed all round at equal distances, with a post at each corner and as few posts as possible.
How many posts are needed?

The spacing must divide both sides, so the largest spacing is HCF(693, 462). Here $693=3^2\times 7\times 11$ and $462=2\times 3\times 7\times 11$, so HCF = $3\times 7\times$ 11 = 231 m. The perimeter is $2\times (693+462)=2310$ m, so the number of posts is 2310 / 231 = 10. Answering 231 gives the spacing instead of the count; 5 uses only one length plus one breadth (1155 / 231).