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Labs / Mathematics
Prime Factorization
Type a whole number and press Split next, or click any highlighted circle, to break it into two factors. Keep going and the tree branches down to its prime leaves — the unique “prime fingerprint” that every integer greater than 1 is built from.
Labs / Mathematics / Prime Factorization
Prime Factorization
Type a whole number and press Split next, or click any highlighted circle, to break it into two factors. Keep going and the tree branches down to its prime leaves — the unique “prime fingerprint” that every integer greater than 1 is built from.
Why it matters
Why explore this?
Mathematics helps us describe patterns precisely and predict what comes next. This model turns an abstract relationship into something you can change and observe.
Explore
Try the model
= 2² × 3 × 5divisors 12prime? noprimes found 0
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
What to try
- Factor 60 with “smallest factor” and then “largest factor” — do you reach the same prime leaves either way?
- Why does the strategy change the tree's shape but never the final list of primes?
- Try 64, then 128, then 256. What pattern shows up in the factorization and the divisor count?
- Can you find a number whose tree is just a single circle? What is special about it?
- Which number under 100 do you think has the most divisors? Test a few and watch the count.
Explain
Make sense of what happened
State the pattern in words, test it with another example, and then connect it to the mathematical rule or representation shown in the model.
Check
Before you leave
What pattern did you observe?
Does the pattern work for another example?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.