# Factor Calculator

> List all the factors and factor pairs of a whole number, with the count, the sum and whether it is prime, perfect, abundant or deficient.

Category: Mathematics · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/factor-calculator

A factor of n is a whole number that divides n with no remainder. Factors come in pairs that multiply to n, so only numbers up to √n need checking.

Also called: Divisor calculator, Factor pairs calculator.

## Inputs
- Whole number (default 36)

## Results
- Factors
- Factor pairs
- Number of factors
- Sum of factors
- Prime factorisation
- Type of number

## Formula

```
If n = p₁^e₁ × p₂^e₂ × …, the number of factors is (e₁ + 1)(e₂ + 1)…, and every factor is p₁^k₁ × p₂^k₂ × … with 0 ≤ kᵢ ≤ eᵢ
```

Where:
- pᵢ: the distinct primes dividing n
- eᵢ: their exponents

## Worked example
1. 36 = 2² × 3², so it has (2 + 1)(2 + 1) = 9 factors.
2. Pairs: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6.
3. Sum: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 36 = 91.

**Result:** 36 has nine factors, 1, 2, 3, 4, 6, 9, 12, 18 and 36, which add up to 91.

## What the result means

A number with exactly two factors is prime. Square numbers have an odd number of factors because one pair repeats. Perfect numbers, such as 6 and 28, equal the sum of their factors other than themselves.

## Assumptions and limits
- Positive factors only; each negative factor is just the negative of a positive one.
- Numbers up to 10¹².

## Questions

### Is 1 a prime number?

No. A prime has exactly two factors, and 1 has only one.

### What is the difference between factors and multiples?

Factors divide into the number (factors of 12 are 1, 2, 3, 4, 6, 12); multiples are the number times a whole number (12, 24, 36, …).

## Related calculators
- [Prime Factorization Calculator](https://calculators.geekmidst.com/calculators/prime-factorization-calculator)
- [Common Factor Calculator](https://calculators.geekmidst.com/calculators/common-factor-calculator)
- [Greatest Common Factor Calculator](https://calculators.geekmidst.com/calculators/greatest-common-factor-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/factor-calculator