What is a divisor of a number?

A divisor (also called a factor) of an integer N is any whole number that divides N with no remainder. For example, the divisors of 12 are 1, 2, 3, 4, 6 and 12, because each of them divides 12 evenly, while 5 is not a divisor since 12 ÷ 5 leaves a remainder. Every number has at least two divisors, 1 and itself, unless the number is 1, which has only one.

What are all the factors of 12?

The factors of 12 are 1, 2, 3, 4, 6 and 12 — six divisors in total. Their sum is 28. You can pair them so each pair multiplies to 12: 1×12, 2×6 and 3×4. Because 12 has more than two divisors it is composite, not prime, and because its proper divisors (1, 2, 3, 4, 6) add up to 16 rather than 12, it is not a perfect number either.

What is a factor pair?

A factor pair is two divisors that multiply to give the original number. For 12 the factor pairs are 1×12, 2×6 and 3×4, and for 36 they are 1×36, 2×18, 3×12, 4×9 and 6×6. A perfect square like 36 has one pair where both numbers are the same (6×6). Factor pairs are how this tool finds divisors quickly: it only checks up to the square root, then reads off the partner for each one.

How do I count the number of divisors?

You can count them directly from the list, or use the prime factorization shortcut: write N as a product of primes raised to powers, add 1 to each exponent, and multiply. For 12 = 2² × 3¹ the count is (2+1) × (1+1) = 6, which matches the six divisors 1, 2, 3, 4, 6, 12. This calculator shows the count for you, but the shortcut is handy to know for an exam.

What is a perfect number?

A perfect number equals the sum of its proper divisors, the divisors below the number itself. The smallest is 6, whose proper divisors 1, 2 and 3 add up to 6. The next is 28 = 1 + 2 + 4 + 7 + 14, then 496 and 8128. Equivalently, the sum of all divisors including the number is twice the number, so σ(6) = 12. This tool flags a perfect number whenever you enter one.

How is this different from a prime factorization tool?

Prime factorization breaks a number into the primes that multiply to make it, like 12 = 2² × 3. This divisors calculator goes a step further and lists every whole number that divides it, including composite divisors such as 4, 6 and 12 themselves, plus the count, the sum and the factor pairs. Use prime factorization when you want the prime building blocks, and this tool when you want the complete set of factors.

Check homework on factors and multiples

A middle-school assignment asks for every factor of 36. Type 36 and read back 1, 2, 3, 4, 6, 9, 12, 18, 36 — nine factors — then confirm the count and the factor pairs match what your child wrote. The perfect-number and prime flags also let you sanity-check the trick questions, like spotting that 28 is perfect or that 37 is prime.

Build factoring exercises as a teacher

You are writing a worksheet on divisors and want examples with a specific number of factors. Try a few values, watch the divisor count, and pick numbers that make the point: 12 for six factors, 36 for a perfect square with an odd count, 6 and 28 for perfect numbers. Share the link so students land on the worked example directly.

Find common dimensions for a layout or grid

You need to arrange 24 tiles into a rectangle. The factor pairs of 24 are 1×24, 2×12, 3×8 and 4×6, so those are your candidate grids. The tool lists every pair at once, which beats dividing by hand to see which arrangements come out even.

Verify a number-theory result quickly

Working through a problem on the sum-of-divisors function σ(n), you want to confirm σ(12) = 28 or that 496 is perfect. Enter the value and the sum and the perfect flag are right there, exact via BigInt, so you can move on without recomputing the list by hand.

Divisors Calculator — All Factors, Count, Sum and Pairs

List every factor of a number — divisor count, sum of divisors, factor pairs, prime and perfect-number check — runs in your browser

Runs locally
Category Calculator
Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.

Positive integer to find divisors of

Up to 16 digits — commas and spaces are ignored, e.g. 12 or 1 234 560

Number of divisors

Sum of divisors

12 is composite.

All divisors (ascending)

1234612

Factor pairs

1 × 122 × 63 × 4

What this tool does

Free divisors calculator that lists every whole number dividing a given integer, not just its prime factors. Type a positive integer and it returns the full divisor list in ascending order, the number of divisors (the τ function), the sum of all divisors (the σ function), and the factor pairs that multiply back to your number, such as 1×12, 2×6 and 3×4 for 12. It also tells you whether the number is prime (only 1 and itself divide it) and whether it is a perfect number, where the proper divisors add up to the number itself, as with 6 = 1 + 2 + 3. The search walks only up to the square root, so even large values stay fast, and every readout is exact through BigInt rather than rounded. Copy the result in one click or share a link that reopens the same number. Everything runs in your browser; nothing you type is uploaded.

Tool details

Input: Numbers; The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output: Live result + Copy; The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy: Browser-side processing; The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share: Shareable URL state; Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget: Initial JS <= 9 KB; No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit: Calculator · Student; Category and role tags drive related tools, internal links, and quick fit checks.

How to use

1. Input

Paste or drop your content into the tool panel.
2. Process

Click the button. All processing is local in your browser.
3. Copy / Download

Copy the result or download to disk in one click.

How Divisors Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

Getting a realistic range before a purchase, plan, workout, or schedule decision.
Comparing scenarios by changing one input at a time.
Turning rough assumptions into a number you can discuss.

Calculation checks

Double-check units, dates, rates, and rounding assumptions.
Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

Real-world use cases

Check homework on factors and multiples
A middle-school assignment asks for every factor of 36. Type 36 and read back 1, 2, 3, 4, 6, 9, 12, 18, 36 — nine factors — then confirm the count and the factor pairs match what your child wrote. The perfect-number and prime flags also let you sanity-check the trick questions, like spotting that 28 is perfect or that 37 is prime.
Build factoring exercises as a teacher
You are writing a worksheet on divisors and want examples with a specific number of factors. Try a few values, watch the divisor count, and pick numbers that make the point: 12 for six factors, 36 for a perfect square with an odd count, 6 and 28 for perfect numbers. Share the link so students land on the worked example directly.
Find common dimensions for a layout or grid
You need to arrange 24 tiles into a rectangle. The factor pairs of 24 are 1×24, 2×12, 3×8 and 4×6, so those are your candidate grids. The tool lists every pair at once, which beats dividing by hand to see which arrangements come out even.
Verify a number-theory result quickly
Working through a problem on the sum-of-divisors function σ(n), you want to confirm σ(12) = 28 or that 496 is perfect. Enter the value and the sum and the perfect flag are right there, exact via BigInt, so you can move on without recomputing the list by hand.

Common pitfalls

Forgetting that 1 and the number itself are both divisors. The full list of factors of 7 is 1 and 7, not just 7. Leaving out 1, or leaving out the number itself, is the most common slip in factor lists and it also throws off the divisor count.
Confusing factors with multiples. Factors divide into the number (the factors of 12 are 1, 2, 3, 4, 6, 12), while multiples are what you get by multiplying it (12, 24, 36, …). They run in opposite directions, so a "factor of 12" is never larger than 12.
Mixing up sum of divisors with sum of proper divisors. The sum of all divisors of 6 is 12, but the sum of its proper divisors (excluding 6) is 6, which is what makes 6 perfect. Read carefully whether a problem counts the number itself.

Privacy

Every calculation — the divisor list, the count, the sum, the factor pairs and the prime and perfect checks — is plain JavaScript running in your browser tab. The number you type never leaves the page and nothing is logged. The one caveat: the shareable link puts your number in the query string, so a link pasted into chat will record that number in the recipient server's access log. For a value you would rather keep private, use the copy button and paste the text instead of sharing the URL.

FAQ

Tool combos

Folks in your role tend to reach for these alongside this tool.

Browse all tools for this role

Divisors Calculator — All Factors, Count, Sum and Pairs

All divisors (ascending)

Factor pairs

What this tool does

Tool details

How to use

1. Input

2. Process

3. Copy / Download

How Divisors Calculator fits into your work

Calculation jobs

Calculation checks

Good next steps

Real-world use cases

Check homework on factors and multiples

Build factoring exercises as a teacher

Find common dimensions for a layout or grid

Verify a number-theory result quickly

Common pitfalls

Privacy

FAQ

Percentage Calculator

Unit Converter

Prime Factorization Calculator

GCD & LCM Calculator

Factorial Calculator

Scientific Calculator

24-Point Solver & Game

555 Timer Calculator

A1C to Blood Glucose Calculator

Add Days to Date Calculator

Age Calculator

Age Difference Calculator