How to use this calculator
- Enter or choose whole number.
- The factors updates as you type. Use Copy result or Share to keep it.
Method
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
- pᵢ
- the distinct primes dividing n
- eᵢ
- their exponents
Worked example
- 36 = 2² × 3², so it has (2 + 1)(2 + 1) = 9 factors.
- Pairs: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6.
- Sum: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 36 = 91.
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, …).