Amicable Numbers Finder
Find all amicable number pairs up to a limit, where each number equals the sum of the other proper divisors, such as 220 and 284.
Last reviewed by the Radiatus Cloud team
Find amicable number pairs, where each equals the sum of the other divisors.
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Find amicable number pairs
Amicable numbers, sometimes called friendly numbers, are two different numbers where each one equals the sum of the proper divisors of the other. This finder searches up to a limit you set and lists every amicable pair it discovers. The smallest and most famous pair is two hundred and twenty and two hundred and eighty-four: the divisors of two hundred and twenty add up to two hundred and eighty-four, and the divisors of two hundred and eighty-four add up to two hundred and twenty.
The search tests each number against the sum of the divisors of its partner to confirm a genuine amicable relationship.
Friendly numbers through the ages
Amicable pairs have intrigued mathematicians since the ancient Greeks, who attached mystical significance to the first pair, and many famous mathematicians sought new pairs over the centuries. They are rarer than perfect numbers, which are in a sense a number being amicable with itself. Beyond the first pair, the next are considerably larger, which is why a search tool makes exploring them practical.
Finding pairs requires summing divisors for many numbers, so very large limits take longer; the tool caps the range to stay responsive. All calculation happens locally in your browser.
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Frequently Asked Questions
What are amicable numbers?
Two different numbers where each equals the sum of the proper divisors of the other, such as two hundred and twenty and two hundred and eighty-four.
What is the smallest amicable pair?
Two hundred and twenty and two hundred and eighty-four, known since antiquity and the first pair this finder reports.
How do they relate to perfect numbers?
A perfect number equals the sum of its own proper divisors, so it is, in a sense, amicable with itself, while amicable pairs involve two distinct numbers.
Why limit the search range?
Summing the divisors of many numbers is work, so a large limit is slow. The tool caps the range to stay responsive in the browser.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Enter an upper limit to find amicable pairs below it.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.