Logic Masters · Ages 11 to 12
Prime Factor Trees
Build factor trees and write each number as a product of primes. Five levels with answer keys.
The learning journey
Every activity is one step. Here is where this one fits.
- PlayLearn the idea in a game
- Practise(you are here)Lock it in on paper
- ReviewCome back and keep it sharp
- MasterTake on a harder challenge
- AchieveEarn a certificate
About Prime Factor Trees
Every whole number above one has exactly one prime factorisation, and the factor tree is how pupils first meet that fact as something they can see rather than take on trust. This worksheet gives a partly drawn tree for each number: the composite at the top, branches splitting downwards, and ringed circles marking the terminal nodes where a prime has been reached. The pupil completes the tree and writes the product of primes underneath, using index notation where a prime repeats. Every number on the page is genuinely composite and has enough prime factors to make a tree worth drawing — a number with only two factors gives a single split, which is not a tree. The branches are generated from the same canonical factorisation that produces the answer key, so a composite can never be left sitting in a terminal position and the product of the leaves always reconstructs the original number. Number sizes grow across the five levels, and the trees deepen with them. Six trees per page with a writing line beneath each. Each level prints as a clean A4 sheet in black and white and downloads with its own separate answer key. Its on-screen twin is Prime Factor Tree Builder.
Common questions
- Can a tree end on a composite number?
- No. The branches are built from the canonical factorisation, so every terminal node is prime by construction.
- Are any of the numbers prime themselves?
- No. A prime has no tree, so every number on the page is composite with enough factors to make a tree worth drawing.
- How are repeated primes written?
- In index notation — so 24 is written as 2^3 × 3.
- How do the levels get harder?
- The numbers grow and the trees deepen, from small composites up to numbers with four or more prime factors.
A hand for grown-ups
- Before you start
- Think of it as groups: "4 × 3" is four groups of three. Have something you can arrange into equal groups.
- While they work
- Skip-counting (3, 6, 9, 12…) is a solid way in before facts are memorised. Let them use it — speed comes later.
- Afterwards
- Spot arrays in real life together — eggs in a box, tiles on a floor. Rows-and-columns is multiplication you can see.
- Watch out for
- Treating it as harder addition and losing track. Grouping objects physically keeps the "equal groups" idea in view.
- Away from the screen
- Lay out objects in rows and columns and count them two ways. Cooking with doubled recipes is multiplication too.
Where to go next
Chosen by the skills this activity practises.