Prime Factorization Calculator
Find the prime factorization of any number. Shows all prime factors, divisors, and whether the number is prime, perfect, abundant, or deficient.
Inputs
Results
Prime Factorization
2^3 × 3^2 × 5
Prime Factors (Expanded)2 × 2 × 2 × 3 × 3 × 5
Is Prime?No
Total Prime Factors6
Unique Prime Factors3
All Divisors1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
Number of Divisors24
Sum of All Divisors1,170
Number ClassificationAbundant number
Factor Tree360
├── 2
└── 180
└── ├── 2
└── └── 90
└── └── ├── 2
└── └── └── 45
└── └── └── ├── 3
└── └── └── └── 15
└── └── └── └── ├── 3
└── └── └── └── └── 5
How to Use This Calculator
- Enter any positive integer in the Number to Factor field (up to the supported maximum).
- The calculator uses trial division to decompose the number into its prime factors (e.g., 60 = 2² × 3 × 5).
- Prime Factorization shows the compact exponential form; Prime Factors (Expanded) lists every prime in the product.
- All Divisors lists every integer that divides the number evenly — useful for finding GCF or LCM manually.
- The Is Prime? output tells you immediately if no factorization exists beyond 1 and the number itself.
- Numbers can be classified as perfect, abundant, or deficient based on the sum of their proper divisors.
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