# Factor Calculator

URL: https://speedycalculator.com/calculators/math/factor/
Last updated: 2026-10-30

> The factor calculator lists every factor (divisor) of a whole number, its factor pairs and prime factorisation, and – if you add a second number – their common factors and greatest common factor.

## Inputs

- Number #1
- Number #2 (optional, 0 to skip)

## Results

- Factors of number #1
- How many factors
- Factor pairs
- Prime factorisation
- Factors of number #2
- Common factors
- Greatest common factor

## Formula

```
d is a factor of n ⇔ n ÷ d leaves no remainder
Number of factors = (e₁ + 1)(e₂ + 1)… for n = p₁^e₁ p₂^e₂ …
```

## Explanation

Factors are the building blocks of multiplication. Listing them helps you simplify fractions, find common denominators, arrange objects in rectangular arrays and solve number puzzles.

### How to use the Factor Calculator

- **Number #1**
- **Number #2 (optional, 0 to skip)**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

The calculator factorises the number into primes and combines the prime powers to generate every divisor, so even large numbers are handled quickly.

### Tips

- Estimate the answer first so you can spot an impossible result.
- Work with whole numbers where possible and place the decimal point at the end.
- Use the order of operations: brackets, powers, multiplication and division, then addition and subtraction.
- For large integers, the calculator works with exact whole-number arithmetic in your browser.

### Common mistakes to avoid

- Misaligning decimal points when adding or subtracting.
- Forgetting the remainder in whole-number division.
- Rounding too early in a multi-step calculation.

## Worked example

Inputs — Number #1: 36; Number #2 (optional, 0 to skip): 48.

Results — **Factors of number #1 = 1, 2, 3, 4, 6, 9, 12, 18, 36**; How many factors = 9; Factor pairs = (1, 36) (2, 18) (3, 12) (4, 9) (6, 6); Prime factorisation = 2² × 3²; Factors of number #2 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48; Common factors = 1, 2, 3, 4, 6, 12.

## Key terms

- **Factor (divisor)**: A whole number that divides another exactly.

## FAQ

**What are the factors of 36?**
1, 2, 3, 4, 6, 9, 12, 18 and 36.

**What is a factor pair?**
Two numbers that multiply to give the number, such as (4, 9) for 36.

**Which numbers have an odd number of factors?**
Perfect squares, because one factor pair repeats (6 × 6).

**Is 1 a factor of every number?**
Yes, and every number is a factor of itself.

**What formula does the Factor Calculator use?**
d is a factor of n ⇔ n ÷ d leaves no remainder.


## Sources

- [OpenStax – Contemporary Mathematics](https://openstax.org/details/books/contemporary-mathematics)
- [Wolfram MathWorld – Prime factorization](https://mathworld.wolfram.com/PrimeFactorization.html)