Build a Factor Tree

Pick a number and break it apart. Click any number that is not yet prime and choose a way to split it into two factors. Keep going until every branch ends in a prime. Those primes, multiplied together, are the number — and there is only one set of them.

Click a boxed number to split it Green leaves are prime — they cannot split further Finish when every leaf is green

Start from

Prime factorisation

Keep splitting until every leaf is prime.

The primes read off the bottom of the tree are the prime factorisation.

Why it is always the same

Try splitting the same number a different way — start 60 as 6 × 10, or as 4 × 15, or as 2 × 30. The tree looks different each time, but the primes at the bottom always come out the same. That is the Fundamental Theorem of Arithmetic: every number has exactly one prime factorisation.

Split a number

Click a boxed number above to see the ways it can split into two factors, then pick one.