Factor Calculator · Practical guide
How to Find the Sum of All Factors of a Number
Add every divisor including 1 and the number itself: for 28 the sum is 1+2+4+7+14+28 = 56.
At a glance
The Basic Method
The sum of all factors means adding every divisor of the number, including 1 and the number itself. For 28, the factors are 1, 2, 4, 7, 14, and 28, so the sum is 56. For 60, the twelve factors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 total 168. The calculator above lists the factors and reports the sum directly.
Interactive tool
Factor Calculator
Enter your own values, then compare the result with the examples below.
Result
Worked Examples
| Number | Factors | Sum |
|---|---|---|
| 12 | 1, 2, 3, 4, 6, 12 | 28 |
| 18 | 1, 2, 3, 6, 9, 18 | 39 |
| 24 | 1, 2, 3, 4, 6, 8, 12, 24 | 60 |
| 28 | 1, 2, 4, 7, 14, 28 | 56 |
| 60 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 | 168 |
Perfect, Abundant, and Deficient Numbers
The sum of factors tells you something classical about the number. Exclude the number itself to get the proper factor sum, then compare:
- Perfect: proper factors sum to the number — 28 (1+2+4+7+14 = 28) and 6 (1+2+3 = 6) are perfect.
- Abundant: proper factors exceed the number — 12 sums to 16, so it is abundant.
- Deficient: proper factors fall short — 16 sums to just 1+2+4+8 = 15. Primes are always deficient, since their only proper factor is 1.
Notice 28 is perfect precisely because its full factor sum (56) is exactly double the number.
A Shortcut for Large Numbers
Listing works for small numbers, but a number like 7,776 has 45 factors. The calculator handles any positive integer up to one trillion and returns the full list, count, and sum instantly — useful for checking perfect-number candidates or homework answers.
Frequently Asked Questions
Does the sum of factors include the number itself?
By convention on this calculator, yes — 1 and the number itself are both included. Some problems ask for the sum of proper factors, which excludes the number itself.
What is the sum of factors of a prime number?
A prime p has only two factors, 1 and p, so the sum is p + 1. For example, the factors of 13 sum to 14.
What is a perfect number?
A number whose proper factors sum to itself, like 6 and 28. Equivalently, the sum of all its factors (including itself) is exactly twice the number. Known perfect numbers are rare and all even ones follow a pattern involving Mersenne primes.
Can the sum of factors be odd?
Yes — the sum is odd exactly when the number is a perfect square or twice a perfect square. For example, the factors of 36 sum to 91.