Enter Input
Tip: The engine supports 64-bit integers. Extremely large values may be slow.
Example Data
| n | Largest Prime Factor | Notes |
|---|---|---|
| 15 | 5 | 15 = 3 × 5 |
| 13195 | 29 | 13195 = 5 × 7 × 13 × 29 |
| 600851475143 | 6857 | Famed composite from a classic problem |
| 9973 | 9973 | Prime input returns itself |
| 1234567890 | 3803 | 2 × 3² × 5 × 3607 × 3803 |
Results
| # | Input n | Largest Prime Factor | Classification | Time (ms) | Details |
|---|---|---|---|---|---|
| No results yet. Compute to see output here. | |||||
Batch Factor Counts
Counts are built from the current results set. “Unique” counts a prime once per input; “With multiplicity” sums exponents.
Formula Used
Largest prime factor L(n) is the greatest prime p such that p | n. We determine L(n) by factoring n into primes and selecting the maximum factor.
- Fast Miller–Rabin checks for probable primality.
- Pollard Rho splits composites into smaller factors efficiently.
- Small-prime trial divisions (2, 3, 5) reduce trivial factors early.
- Recursively factor the co-factors until all parts are prime.
Time complexity is sub-exponential in the worst case but performs very well for 64-bit integers in practice.
How to Use
- Enter a single integer or paste many integers in batch.
- Optionally check Show steps to display factorization progress.
- Click Compute to process and populate the results table.
- Use Download CSV or Download PDF to export results.
- Use the chart to see prime frequencies across the batch.
Note: Inputs less than 2 have no prime factors. Extremely large values may exceed server limits.
FAQs
If n is prime, the largest prime factor equals n itself, and the classification shows Prime.
The engine targets 64-bit integers on typical servers. Inputs beyond this range may fail or be very slow.
A deterministic Miller–Rabin configuration for 64-bit primality checks plus Pollard Rho for finding nontrivial factors, with small-prime trial division.
No. Prime factors are defined for integers n ≥ 2. For negatives, consider the absolute value’s factors and a sign separately.
To keep output readable, steps summarize key events: small-prime reductions and factors discovered by Pollard Rho.
Yes, but be mindful of server timeouts. Consider batching requests or increasing execution limits for large workloads.
No special math extensions are required. Everything runs with standard integer operations on a typical installation.