Prime Factorization Calculator
Find the prime factors, divisors, factor pairs, and number properties of any integer up to 10¹².
Prime Factorization
360 = 23 × 32 × 5
Number Properties
Totient φ(n)96
Divisor Sum1,170
ClassificationAbundant
All Divisors (24)
1234568910121518202430364045607290120180360
Factor Pairs (12)
1×360
2×180
3×120
4×90
5×72
6×60
8×45
9×40
10×36
12×30
15×24
18×20
Factorization Visualizer
How it worksThe tree recursively splits each composite number into its smallest prime factor (left) and the remaining quotient (right) until only primes remain.
What is Prime Factorization?
Prime factorization expresses any integer as a unique product of prime numbers — called the fundamental theorem of arithmetic. For example, 360 = 2³ × 3² × 5. This calculator uses trial division up to the square root of the input, which is exact and fast for values up to a trillion. From the prime factors it also derives the full divisor list and factor pairs.
Related tools: GCD & LCM Calculator, Prime Number Checker, and the Base Converter.
Private & free — this tool runs entirely in your browser.
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