Prime Factor Tree Builder

About Prime Factor Tree Builder

Prime Factor Tree Builder puts a number at the top of a tree and asks the child to break it apart until only primes remain. Building it as an actual tree rather than a list is deliberate, because the shape carries an idea the list hides: whichever route you take down, you arrive at the same primes. Thirty-six split as six times six and thirty-six split as four times nine look like completely different trees for two rows, and then produce exactly the same four numbers at the bottom. That is the fundamental theorem of arithmetic, met informally and years before anyone puts a name to it, and a student who has noticed it for themselves has a much firmer grip on why prime factorisation is worth doing at all. And it is worth doing: prime factors are how highest common factors and lowest common multiples are found, how fractions are simplified reliably rather than by trial and error, and how surds are broken down two years later. A student who cannot factorise quickly is slow at all three, and the slowness looks like weakness at fractions or at surds rather than what it actually is. Levels one and two give the middle row of the tree so the child produces only the primes; from the third level the whole tree is theirs. Primes stay within two, three, five and seven. Everything is operable by tap or keyboard, and the empty spaces in the tree shape are treated as decoration rather than as boxes to fill. Free, no sign-up, no advertising to children.