amicable numbers
A pair of numbers having the property that the sum of the divisors of each, excluding itself, is equal to the other number.

The factors of 220, excluding 220 itself, are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110 and sum to 284; the factors of 284, excluding 284 itself, are 1, 2, 4, 71, and 142, and sum to 220; hence 220 and 284 are amicable numbers.


Wikipedia foundation.

Look at other dictionaries:

  • Amicable numbers — Amicable Am i*ca*ble, a. [L. amicabilis, fr. amicus friend, fr. amare to love. See {Amiable}.] Friendly; proceeding from, or exhibiting, friendliness; after the manner of friends; peaceable; as, an amicable disposition, or arrangement. [1913… …   The Collaborative International Dictionary of English

  • amicable numbers — plural noun (mathematics) see ↑friendly numbers under ↑friend • • • Main Entry: ↑amicable …   Useful english dictionary

  • Amicable number — Amicable numbers are two different numbers so related that the sum of the proper divisors of the one is equal to the other, one being considered as a proper divisor but not the number itself. Such a pair is (220, 284); for the proper divisors of… …   Wikipedia

  • Amicable — Am i*ca*ble, a. [L. amicabilis, fr. amicus friend, fr. amare to love. See {Amiable}.] Friendly; proceeding from, or exhibiting, friendliness; after the manner of friends; peaceable; as, an amicable disposition, or arrangement. [1913 Webster] That …   The Collaborative International Dictionary of English

  • Amicable action — Amicable Am i*ca*ble, a. [L. amicabilis, fr. amicus friend, fr. amare to love. See {Amiable}.] Friendly; proceeding from, or exhibiting, friendliness; after the manner of friends; peaceable; as, an amicable disposition, or arrangement. [1913… …   The Collaborative International Dictionary of English

  • amicable number — noun Either of a pair of amicable numbers …   Wiktionary

  • amicable number — noun : either of two numbers each of which is equal to the sum of all the submultiples of the other * * * Math. either of a pair of positive integers in which each member is equal to the sum of the submultiples of the other, as 220 and 284 …   Useful english dictionary

  • friendly numbers — plural noun (mathematics) Pairs of numbers each of which is the sum of the factors of the other, including unity (also called amicable numbers; cf ↑perfect number) • • • Main Entry: ↑friend …   Useful english dictionary

  • mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium

  • number theory — Math. the study of integers and their relation to one another. Also called theory of numbers. [1910 15] * * * Branch of mathematics concerned with properties of and relations among integers. It is a popular subject among amateur mathematicians… …   Universalium

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”