Factor Tree

Choose a mode

The number sits at the top of the tree and splits into two branches. Use the −/+ buttons (or drag right to raise, left to lower) to set the left factor. The right branch shows the partner you get by dividing. When the factor divides the number evenly it turns green; otherwise a red question mark appears. Then press Check

3D math game · Best for grades 3-5

Factor Tree

Factor Tree challenges students to split a composite number by choosing two factors whose product equals it, building branches downward until every end-leaf is a prime. The visual tree makes the abstract idea of prime factorisation a concrete hands-on process rather than a rote algorithm.

What students practice

Factor Tree builds understanding of divisibility, prime numbers, and the Fundamental Theorem of Arithmetic — that every whole number has exactly one prime factorisation. Students develop systematic factor-pair thinking rather than guessing, and connect multiplication to division as inverse operations.

  1. Read the target number shown at the top of the tree.
  2. Use −/+ or drag to set the left factor; the right factor updates automatically by division.
  3. Check that the left factor divides the number evenly — it turns green when correct.
  4. Press Check to confirm the factorisation of the current node.

How to use it at home or in class

To factorise 24: choose 4 and 6. Then split 4 into 2×2 and 6 into 2×3. All leaves are prime (2, 2, 2, 3), confirming that 24=2³×3 regardless of which factor pair the student chose first.

Students often choose 1 as a factor, which is not allowed, or stop splitting when they reach a composite number. The tree highlights non-prime leaves in a different colour, prompting further splitting until every branch ends in a prime.

Use it for individual practice, paired work, or a short class demonstration before worksheets.

Start with the game above, then continue with written practice to reinforce the skill.

Common questions

Why does the tree always produce the same prime factors no matter which pair I start with?
This is the Fundamental Theorem of Arithmetic: every number has a unique prime factorisation. Starting with different factor pairs gives different tree shapes but identical prime leaves — a key discovery the game is designed to surface.
Which grades is Factor Tree for?
Grades 3–5, where students first encounter divisibility rules, prime vs. composite numbers, and need to understand the multiplicative structure of whole numbers.
Can a prime number be entered at the top of the tree?
Primes are not used as roots in this game because they cannot be split further. The game selects composite numbers, so every round has at least one valid factor pair to find.