How to play Factor Trail

Find the only trail from start to flag, stepping across or down to numbers that follow the rule. Also known as Factor maze.

The rules

Start on the ▶ square and finish on the ⚑ square.
Each step goes across or down to a neighbouring square — never diagonally, never back onto your trail.
Factors & multiples: the next number must divide the current one, or be divisible by it. Primes: step only on primes. Times table: step only on multiples of the chosen number.
Exactly one trail works.

Choose a rule — factors & multiples, primes, or a times table — and a grid size, then press New Puzzle.
Start on the ▶ square. Tap (or drag across) squares next to the end of your trail to extend it, across or down.
Tap a square already on your trail to go back to it.
Reach the ⚑ flag. Hint shows the next step and why the other neighbours don’t work.

You are on 12. Its neighbours are 36, 25 and 7. 36 is 12 × 3, a multiple — that works. 25 and 7 are neither factors nor multiples of 12.

So step to 36. From 36 the next number might be 9 (a factor) or 72 (a multiple).

Use divisibility tests. Even numbers end in 0, 2, 4, 6, 8; multiples of 3 have digits that add to a multiple of 3; multiples of 5 end in 0 or 5.
Watch for big primes. In factors & multiples, a prime like 53 only links to 1, itself and its multiples — a prime next to you usually isn’t the way.
Check every neighbour. At each step usually only one neighbour works — rule the others out.
Look from the flag too. Working backwards from the finish can show which way the trail must come.

Factor Trail was made for this site, turning number facts into a maze with exactly one way through.

Is 1 a prime?

No — a prime has exactly two factors, 1 and itself. 1 has only one.

Can the trail touch itself?

The trail never runs alongside itself, so there is never a shortcut.

Is there always one trail?

Yes — every number off the trail breaks the rule with all its neighbours.