Calculate a Factor Tree
Example Data Table
| Number | One Factor Tree Path | Prime Factors | Prime Power Form | Total Divisors |
|---|---|---|---|---|
| 48 | 48 = 6 × 8, 6 = 2 × 3, 8 = 2 × 4, 4 = 2 × 2 | 2 × 2 × 2 × 2 × 3 | 24 × 3 | 10 |
| 72 | 72 = 8 × 9, 8 = 2 × 4, 4 = 2 × 2, 9 = 3 × 3 | 2 × 2 × 2 × 3 × 3 | 23 × 32 | 12 |
| 225 | 225 = 15 × 15, 15 = 3 × 5, 15 = 3 × 5 | 3 × 3 × 5 × 5 | 32 × 52 | 9 |
| 840 | 840 = 28 × 30, 28 = 4 × 7, 4 = 2 × 2, 30 = 5 × 6, 6 = 2 × 3 | 2 × 2 × 2 × 3 × 5 × 7 | 23 × 3 × 5 × 7 | 32 |
Formula Used
Core factor tree rule: Start with a whole number n. Split it into factor pairs n = a × b. Keep splitting each composite branch until every leaf is prime.
Prime power form: If a number contains repeated primes, write it as n = p1e1 × p2e2 × ...
Divisor count: If the exponents are e1, e2, e3..., then total divisors = (e1 + 1)(e2 + 1)(e3 + 1)...
Sum of divisors: Multiply each geometric series term: ((pe+1 - 1) / (p - 1)) across all prime factors.
How to Use This Calculator
- Enter any integer greater than 1.
- Select how you want composite numbers split during the tree build.
- Choose whether prime factors should display in ascending or descending order.
- Turn optional outputs on or off, including all factors, steps, and verification.
- Press Generate Factor Tree to show the result above the form.
- Review the factor tree, prime powers, divisor metrics, and Plotly graphs.
- Use the export buttons to download a CSV or PDF summary.
FAQs
1. What is a factor tree?
A factor tree breaks a whole number into smaller factor pairs until every ending value is prime. It is a visual way to see prime factorization clearly.
2. Why do different trees sometimes look different?
Different factor pairs can be chosen first, so the branch layout may change. The final prime factors remain identical because prime factorization is unique.
3. Can this calculator handle prime numbers?
Yes. If the input is already prime, the tree ends immediately with one leaf. The prime factorization is simply the number itself.
4. What does prime power form mean?
Prime power form groups repeated prime factors using exponents. For example, 72 becomes 23 × 32, which is shorter than writing every repeated factor separately.
5. Why does the calculator show total divisors?
Once prime exponents are known, you can quickly count all divisors using the exponent rule. This makes the factor tree useful for more than basic decomposition.
6. What is the difference between factors and prime factors?
Factors are all whole numbers that divide the input exactly. Prime factors are only the prime numbers that multiply together to recreate the input.
7. When should I use balanced splitting?
Balanced splitting works well when you want a visually compact tree. It picks factor pairs closer to each other, making the graph easier to read.
8. Does the multiplication verification matter?
Yes. Verification confirms that the listed prime factors multiply back to the original number. It is a quick check against entry mistakes or misread branches.