Steps without the calculator
Factor the magnitude, add one to every prime exponent, and multiply those adjusted exponents.
Math calculator
Divisor Count Calculator
Count the positive divisors of a nonzero integer from its prime exponents. The page traces how the inputs become number of divisors before rounding.
Divisor Count inputs
Enter the source values
A worked example
Since 360 = 2³×3²×5, its divisor count is (3+1)(2+1)(1+1)=24. This Divisor Count example can be compared with prime exponents.
Situations that fit the model
Divisor counts help identify highly composite numbers, compare grouping possibilities, and analyze integer sequences.
Why this relationship works
If n has prime factorization p₁^a₁p₂^a₂…, every divisor chooses an exponent from zero through each a. Multiplying the choice counts gives the divisor total. Divisor Count also connects with complete factor list.
For this page, divisor count is interpreted under the stated convention and input order.
Mistakes worth catching
The count here includes one and the number itself and uses positive divisors. Zero has no finite divisor count.
A one-input Divisor Count trial checks the expected behavior of divisor count.
Meaning, scale, and reporting
Transfer the source entries one at a time under nonzero integer, keeping any units visible in your notes. This page can validate numerical ranges, but only the reader can confirm that each entry represents the intended quantity.
Adding a previously absent prime factor doubles the count; raising an existing exponent changes only one multiplier. Trying a nearby input should follow this pattern; otherwise inspect the field assignment.
Attach units and the name number of divisors whenever the answer leaves this page. A rounded value is suitable for presentation, while retained working digits are safer for a dependent calculation.
This page counts factors without listing them; the factor calculator displays the actual divisor values. That neighboring measure needs its own setup rather than a relabeled answer.
Copying only the decimal discards the setup. Pair the number of divisors with nonzero integer and the unit convention so another reader can reconstruct its meaning.
What the count reveals
An odd divisor count identifies a perfect square, because every nonsquare factor has a different partner while the square root remains unpaired. The count alone does not identify the factors, but it gives a compact structural clue and a useful check on a separately prepared factor list.
Questions about Divisor Count
Does a prime have two divisors?
Yes.
Why add one to each exponent?
A divisor may use exponent zero through the exponent in n.
Is a perfect square’s divisor count odd?
Yes, because its square-root factor is unpaired.