Calculator
Example Data Table
| Number | Prime Factorization | Repeated Prime Factors | Total Divisors |
|---|---|---|---|
| 36 | 2² × 3² | 2 × 2 × 3 × 3 | 9 |
| 72 | 2³ × 3² | 2 × 2 × 2 × 3 × 3 | 12 |
| 84 | 2² × 3 × 7 | 2 × 2 × 3 × 7 | 12 |
| 225 | 3² × 5² | 3 × 3 × 5 × 5 | 9 |
Formula Used
A factor tree repeatedly splits a composite number into smaller factors.
n = a × b
Keep splitting each composite branch until every end value is prime.
n = p₁e₁ × p₂e₂ × ... × pₖeₖ
The calculator also counts divisors from the prime exponents.
d(n) = (e₁ + 1)(e₂ + 1)...(eₖ + 1)
Verification multiplies all repeated prime factors to recover the original number.
How to Use This Calculator
- Enter a positive integer greater than 1.
- Choose how the tree should split each composite value.
- Select ascending or descending prime display order.
- Pick a Plotly graph mode for exponents or branches.
- Enable factor pairs or verification, then submit the form.
- Review the result block, tree, tables, and graph above.
- Use CSV or PDF export for saving your work.
FAQs
1. What is a factor tree?
A factor tree breaks a whole number into smaller factors. The process continues until every branch ends with prime numbers only.
2. Why do factor trees end with primes?
Prime numbers cannot be split into smaller whole-number factors except 1 and themselves. They are the final building blocks of the original number.
3. Can one number have different factor tree shapes?
Yes. Different branches can appear depending on the chosen split order. The prime factorization stays the same, even when the tree looks different.
4. What does the exponent chart show?
The bar chart shows how many times each prime appears. Larger bars mean that prime repeats more often in the final factorization.
5. What is split verification?
Split verification checks each branch by multiplication. It confirms that every parent value equals the product of its two child factors.
6. Does this work for prime numbers too?
Yes. A prime number returns a one-node tree because it already has no composite branches to break further.
7. Why are negative numbers excluded?
This page focuses on standard positive-integer factor trees. Negative values add sign handling, which is usually taught separately from basic factor decomposition.
8. What do the CSV and PDF exports save?
CSV saves summary fields, exponents, steps, and optional pairs. PDF captures the visible result area, including the tree and graph.