Factor Calculator
Find all factors and factor pairs of a number
About the Factor Calculator
Every whole number can be broken down into the smaller numbers that divide it evenly — its factors. This calculator lists all of them, pairs them up, counts them, sums them, and tells you whether the number is prime, composite, or even a perfect number.
Students use it across number theory and fraction work; puzzle solvers and programmers use it when divisibility matters. The factor pairs are especially handy for problems like finding rectangle dimensions for a given area, and the perfect-number check adds a touch of mathematical curiosity that pure factor lists miss.
How to Use the Factor Calculator
- Enter a positive whole number.
- Read the full list of its factors.
- Review the factor pairs, each multiplying to your number.
- Check the extras: factor count, sum of factors, prime-or-composite type, and whether it is a perfect number.
Why Use ToolForge’s Factor Calculator
- It lists factor pairs with multiplication notation, not just a flat list, which suits problems like sizing rectangles for a given area.
- It classifies the number as prime or composite and flags perfect numbers, going beyond a bare factor list.
- It reports the count and sum of factors, useful shortcuts for many number-theory problems.
- All computation stays in your browser with no account.
Frequently Asked Questions
What is the difference between factors and prime factors?
Factors are all the numbers that divide evenly into your number, including 1 and the number itself. Prime factors are only the prime numbers among them, which multiply together to make the number. This tool lists all factors; a prime factorization tool isolates the primes.
What makes a number prime or composite?
A prime number has exactly two factors, 1 and itself. A composite number has more than two. The calculator counts the factors and labels the number accordingly — note that 1 is neither prime nor composite by definition.
What is a perfect number?
A perfect number equals the sum of its proper divisors (all its factors except itself). The smallest is 6, since 1 + 2 + 3 = 6. They are rare, and the calculator flags one when you happen to enter it.
How do factor pairs help with real problems?
Each pair multiplies to your number, so they map directly to questions like "what rectangle dimensions give this area?" or "how can I arrange this many items into equal rows?" The calculator lists every pair, saving you from testing divisors one by one.
