Factor CalculatorFree online math calculator — instant results, no sign-up
All factors and factor pairs of a number.
About the Factor Calculator
The Factor Calculator finds all positive integer divisors of a given whole number along with the total count of those factors. It is commonly used by students, educators, and programmers working on divisibility problems, fraction simplification, or algebraic factoring.
- Number
- The positive integer to be factored (typically an integer greater than or equal to 1).
Formula and method
d is a factor of x if x mod d = 0, where 1 <= d <= x
- xThe input integer to be factored
- dAn integer divisor that divides x with zero remainder
- modModulo operation representing the remainder of division
The tool evaluates potential integer divisors up to the input value to identify all integers that divide the number evenly without a remainder. It compiles the qualifying divisors into an ordered list and counts the total number of factors.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Number60
Results
- Factors1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Count12
How to use the Factor Calculator
- 1Enter a positive integer into the Number field.
- 2The tool tests integer divisors from 1 up to the number.
- 3All values where the remainder equals zero are collected and sorted in ascending order.
- 4The complete list of factors and the total count of factors are displayed.
Reading your result
The 'Factors' output lists every positive integer that divides the input number evenly, presented in ascending order. The 'Count' displays the total number of divisors; a count of 2 indicates that the number is prime (divisible only by 1 and itself).
Limitations
This calculator lists only positive whole-number factors and does not display negative factors (such as -1, -2). It does not compute prime factorizations with exponents or handle non-integer decimal inputs.
Common questions
What is the difference between a factor and a prime factor?+
A factor is any integer that divides a number without a remainder. A prime factor is a factor that is also a prime number (such as 2, 3, or 5 for the number 60).
How can I find factor pairs from the output list?+
Pair the first factor with the last factor, the second with the second-to-last, and so on. For 60, pairs are (1, 60), (2, 30), (3, 20), (4, 15), (5, 12), and (6, 10).
Why does a square number have an odd count of factors?+
Most factors come in distinct pairs (a × b = x), but a perfect square has one pair where both factors are identical (such as 6 × 6 = 36), resulting in an odd total count.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.