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Factor Calculator

Every factor of a number, in pairs, with prime factors marked.

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All factors

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Factor pairs

Factors always come in pairs, mirrored around the square root — which is why you only need to test divisors up to that point.

Smaller×LargerBoth prime?

Number of factors

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Properties

Prime factorisation—
Prime factors—
Sum of all factors—
Sum of proper factors—

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Perfect, abundant or deficient

A factor divides evenly with no remainder; a multiple is what you get by multiplying. A number is perfect when its proper factors sum to itself — 6 is perfect because 1 + 2 + 3 = 6, and the next one is 28. Perfect numbers are rare enough that only 51 are known.

Quick Tool Overview

The Factor Calculator lists every whole number that divides evenly into a given number, arranged in the pairs that multiply back to it, with prime factors marked and the number classified as perfect, abundant or deficient.

What it does
Lists every factor of a number, in pairs
You give it
Any positive whole number
You get back
Factor pairs, prime factors, count, sum and class
Best for
Homework, factoring practice and number properties
Calculators Free, unlimited use No sign-up Runs in your browser

About the Factor Calculator

List every whole number that divides evenly into a given number, arranged in the pairs that multiply back to it. Prime factors are marked within the list, and the total count and sum of factors are reported.

Presenting factors as pairs rather than a flat list makes the structure obvious: they always come two at a time, mirrored around the square root, which is why you only ever need to test divisors up to that point. The sum of the proper factors also classifies the number as perfect, abundant or deficient — 6 is perfect because 1 + 2 + 3 equals 6 exactly, and perfect numbers are rare enough that the next one is 28.

Key features of the Factor Calculator

Factors shown in pairs

Each pair multiplies back to your number, which makes the mirroring around the square root obvious.

Primes marked in the list

You can see which factors are prime without running a second tool.

Perfect, abundant or deficient

The sum of proper factors classifies the number — 6 is perfect, and the next one is 28.

Count and sum included

How many factors there are and what they total, both common follow-up questions.

Only tests to the square root

Because every divisor above it already has a partner below, so large numbers stay fast.

How to use the Factor Calculator

  1. 1

    Enter a whole number

    Any positive integer.

  2. 2

    Read the factor pairs

    Each pair multiplies back to your number, mirrored around the square root.

  3. 3

    Note the primes

    Prime factors are marked, and the prime factorisation is shown separately.

  4. 4

    Check the classification

    Whether the number is perfect, abundant or deficient, from the sum of its proper factors.

Frequently asked questions

A whole number that divides evenly into another with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12.

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