Factors of a Number Calculator
Enter any positive whole number to instantly list all of its factors, count them, add them up, and see every factor pair.
Total divisors of 60
- 1
Square-root search limit
⌊√60⌋ = 7Only test i = 1 … ⌊√n⌋; each divisor i below the root has a complement n/i above it. - 2
Factor pairs (i × n/i = n)
1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, … = 6 pairs - 3
Total factor count
6 × 2 = 12
How does this calculator work?
The factors of a number n are all positive integers that divide it evenly. Enter a positive whole number and this tool lists every factor, counts them, sums them, and shows the factor pairs (i × n/i = n). It searches only up to √n for speed and includes 1 and n.
Formula
How this is calculated
A factor (or divisor) of a number n is any positive integer that divides n exactly, leaving no remainder. This calculator takes a single positive integer n and finds every such divisor.
Rather than testing all numbers from 1 to n, it loops i from 1 up to the integer square root of n. Whenever n is divisible by i (n mod i = 0), both i and its complement n/i are factors, so the pair is collected at once. This cuts the work from n steps to about √n steps. The collected values are de-duplicated (perfect squares yield the same factor twice) and sorted ascending to produce the final divisor list.
The factor count is simply the length of that list, the factor sum is the total of all divisors, and the factor pairs show each divisor alongside the value that multiplies with it to give n. The input must be a positive whole number; fractions, zero, and negatives have no well-defined factor list here, and extremely large inputs are rejected to keep the search fast.
Frequently asked questions
A factor divides a number exactly (e.g., 4 is a factor of 12), while a multiple is the result of multiplying a number by an integer (e.g., 24 is a multiple of 12). Factors are always less than or equal to the number; multiples are greater than or equal to it.
Every positive integer is divisible by 1 and by itself, so 1 and n are always in the list. A prime number has exactly these two factors and no others.
By checking only divisors up to the square root of n. Each divisor i below the square root has a matching partner n/i above it, so both can be recorded together, halving the search effort.
Also known as
TG we-Calculate Editorial Team. (2026). Factors of a Number Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/factors-of-a-number-calculator
TG we-Calculate Editorial Team. "Factors of a Number Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/factors-of-a-number-calculator.
TG we-Calculate Editorial Team, "Factors of a Number Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/factors-of-a-number-calculator
@misc{wecalculate_factors_of_a_number_calculator, title = {Factors of a Number Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/factors-of-a-number-calculator}}, year = {2026}, note = {TG we-Calculate} }
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