Factors Calculator (All Divisors of a Number)
Enter a whole number to list all of its factors.
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Factors
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Number of factors
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Sum of factors
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Sum of proper factors (excluding the number)
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Classification
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Factor pairs
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Factors Calculator (All Divisors of a Number) by TheCalcTools
How the Factors Calculator (All Divisors of a Number) works
Factors come in pairs that multiply to n, so they are found from the prime factorization by combining primes in every possible way.
A number is perfect when its proper factors add up to itself (6 = 1 + 2 + 3), abundant when they add up to more, and deficient when they add up to less.
The formula
σ(n) = Π (p^(a+1) − 1) ÷ (p − 1)
Worked example
Using the default values shown in the calculator:
| Whole number | 220 |
|---|
- The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220.
- Proper factors add up to 284, so 220 is Abundant.
Result:
| Factors | 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220 |
|---|---|
| Number of factors | 12 |
| Sum of factors | 504 |
| Sum of proper factors (excluding the number) | 284 |
| Classification | Abundant |
| Factor pairs | 6 |
Frequently asked questions
What are the factors of 220?
1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110 and 220. Its proper factors add up to 284, and 284’s add up to 220: an amicable pair.
Sources and further reading
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