Enter Numbers and Options
Formula Used
Every factor divides the number without leaving a remainder. Factor pairs multiply to produce the original whole number. Prime factorization expresses that number using only prime factors.
- Factor test: n mod d = 0
- Divisor count: (a₁ + 1)(a₂ + 1)…(aₖ + 1)
- Divisor sum: ∏[(pᵢ^(aᵢ+1) − 1) ÷ (pᵢ − 1)]
- GCF uses shared prime factors with minimum exponents.
- LCM uses every prime factor with maximum exponents.
How to Use
- Enter one or several nonzero whole numbers.
- Choose factor filters, range limits, and sorting.
- Select optional negative, proper, prime, or common factors.
- Press Calculate Factors to create detailed results.
- Copy, export, print, or save the calculation.
Example Data
| Input | Main Purpose | Expected Highlight |
|---|---|---|
| 24 | All factors | 1, 2, 3, 4, 6, 8, 12, 24 |
| 36 | Factor pairs | 6 × 6 is the square pair |
| 360 | Prime factorization | 2³ × 3² × 5 |
| 18, 30 | Common factors | GCF equals 6 |
| 12, 18, 24 | GCF and LCM | GCF 6 and LCM 72 |
| -20 | Negative factor pairs | Positive and negative combinations |
Saved Calculation History
Frequently Asked Questions
What is a factor?
A factor divides a number without any remainder. Factors appear in matching multiplication pairs. Each pair produces the original number exactly.
Does zero have factors?
Every nonzero integer divides zero without a remainder. Therefore, zero has infinitely many possible divisors. This calculator excludes zero for useful finite results.
Can negative numbers have factors?
Negative numbers have positive and negative factor combinations. Their factor pairs must produce a negative product. Enable negative factors to display both signs.
What are proper factors?
Proper factors exclude the positive number itself. They still include one for positive integers. Their sum supports abundance classification.
How is prime factorization different?
Prime factorization uses prime numbers only. Repeated primes appear with exponent notation. Their product always rebuilds the original magnitude.
What is the GCF?
The GCF is the largest shared factor. It divides every selected number exactly. It helps simplify ratios and fractions.
What is the LCM?
The LCM is the smallest shared positive multiple. Every selected number divides it evenly. It helps combine repeating schedules and denominators.
What makes a number abundant?
An abundant number has a larger proper-factor sum. A perfect number has an equal proper-factor sum. A deficient number has a smaller sum.
Why is there an input limit?
Large inputs require more factor testing and processing. Practical limits keep the page responsive. The current maximum is one billion per number.