Factor Pairs Calculator
List all factors (divisors) of a number and its factor pairs. See how many divisors it has and whether it is prime or a perfect square.
Last reviewed by the Radiatus Cloud team
List every factor of a number and all the pairs that multiply to give it.
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List all factors and factor pairs
A factor, or divisor, of a whole number is any number that divides it exactly with no remainder. The Factor Pairs Calculator finds every factor of the number you enter and arranges them into factor pairs, the pairs of numbers that multiply together to give your number. For thirty-six the factors are one, two, three, four, six, nine, twelve, eighteen and thirty-six, and the factor pairs include one times thirty-six, two times eighteen, and six times six.
It works efficiently by testing divisors only up to the square root of the number and pairing each one with its partner, so even large numbers are factored quickly.
Why factors matter
Factors are fundamental to arithmetic. Students use them to simplify fractions, find common denominators and factor expressions. The calculator also tells you whether the number is prime, meaning it has exactly two factors, and whether it is a perfect square, meaning one factor pair consists of a number multiplied by itself.
Factor pairs are especially useful in geometry and design, where you need the whole-number dimensions of a rectangle with a given area. Enter any positive whole number up to a trillion. All calculation happens locally in your browser.
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Frequently Asked Questions
What is the difference between a factor and a multiple?
A factor divides a number exactly, while a multiple is the result of multiplying it. Six is a factor of twelve, and twelve is a multiple of six.
What are factor pairs?
They are pairs of factors that multiply to give the number, such as three times twelve and four times nine for thirty-six.
How does it know if a number is prime?
A number greater than one is prime when it has exactly two factors, one and itself. The tool checks the factor count to decide.
Why is a perfect square highlighted?
A perfect square has a factor pair made of the same number twice, like six times six for thirty-six, so its middle pair is a single repeated factor.
Is there a maximum number?
You can factor numbers up to one trillion. The square-root method keeps even large numbers fast to process in your browser.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Enter a positive whole number to list all its factors and factor pairs.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.
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