amicable number

noun

mathematics
: either of a pair of numbers each of which equals the sum of the different exact divisors of the other excluding the number itself

Note: 220 and 284 are examples of amicable numbers. The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110, which sum to 284, while the factors of 284 are 1, 2, 4, 71, and 142, which sum to 220.

Word History

First Known Use

circa 1763, in the meaning defined above

Time Traveler
The first known use of amicable number was circa 1763

Love words?

You must — there are over 200,000 words in our free online dictionary, but you are looking for one that’s only in the Merriam-Webster Unabridged Dictionary.

Start your free trial today and get unlimited access to America's largest dictionary, with:

  • More than 250,000 words that aren't in our free dictionary
  • Expanded definitions, etymologies, and usage notes
  • Advanced search features
  • Ad free!

Dictionary Entries Near amicable number

Cite this Entry

“Amicable number.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/amicable%20number. Accessed 23 Nov. 2024.

Love words? Need even more definitions?

Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free!