Prime factorization writes |n| as a product of primes—e.g. 360 = 2³×3²×5. It underpins GCF, LCM, simplifying fractions, and divisibility. Enter one non-zero integer for power notation and a chip wall of prime factors.
How to use
- Enter non-zero n (sign ignored for factors).
- Read product notation and factor chips.
- Compare lists → GCF; combine multiples → LCM.
Short division idea
Divide by 2, then 3, 5, 7… while possible; chips summarize counts.
Examples
360 → 2³×3²×5; 84 → 2²×3×7; prime 17 → 17; 1 → no primes.
Links
Shared primes at lower powers → GCF. Arithmetic → fraction calculator; decimal swap → decimal ↔ fraction.
Frequently asked questions
Same as listing all factors?
Not quite—this page stops at primes with powers (12=2²×3). Listing every factor 1…12 is a different task.
What about 1 and prime n?
n=1 has no prime factors. A prime p factors as p alone—one chip.
Negative numbers?
Factorization uses |n|; sign does not change the prime multiset.
Short division by hand?
Divide by 2, then 3, 5, 7… while possible; power notation compresses that trail.
Why is 360 a classic example?
360 = 2³×3²×5 mixes several primes and powers—good practice. Try 360 or your homework n.
Can I save my inputs?
Yes. Copy link below the form keeps your current inputs so you can share the scenario or save it for later.