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# What are friendly numbers?

Question #66676. Asked by darkpresence. (Jun 08 06 1:57 PM)

EggoWillie

Numbers that cuddle... No, my Trig teacher always said that whole numbers or integers that would divide evenly by whatever the problem dictated were friendly. This isn't a real math term, but he used it liberally. EX. 2x + 4 = 8; in this you could call 2 a friendly number because it works out.

 Jun 08 06, 2:05 PM
zbeckabee

A friendly number is a number that is a member of a friendly pair, or higher-order friendly tuple.

http://mathworld.wolfram.com/FriendlyNumber.html

 Jun 08 06, 2:39 PM
darkpresence

My reference book (very old fashioned I know, sorry no online link)) says "Pythagoras regarded two numbers as friendly if each was the sum of the other's divisors. The Greeks were aware of just one such pair, 220 and 284. The divisors of 220 (1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110) add up to 284, while the divisors of 284 (1, 2, 4, 71, 142) add up to 220. Not until 1636 was another pair of friendly numbers -- 17,296 and 18,416 -- discovered by the French mathematician Pierre de Fermat. However, by the middle of the 19th century, the number of known friendly pairs totalled more than 60. Incredibly, the second-lowest pair of all had been missed. In 1867 a 16-year-old Italian, Nicolo Paganini, demonstrated that 1,184 and 1,210 are friendly.
There are questions associated with friendly numbers too. All known examples consist of either two odd or two even numbers. Are pairs consisting of an odd and an even number possible? Why are all the odd friendly numbers multiples of three?" (Reader's Digest Facts And Fallacies)

 Jun 08 06, 8:41 PM
Gnomon

Most maths books use the term "amicable" rather than "friendly" for these numbers that Pythagoras defined.

 Jun 09 06, 2:49 AM
chemyth479

A friendly number (they're actually called compatible numbers) that are easy to add, usually have a sum of a multiple of ten. For example, 4 and 6 are compatible numbers.

 Jun 09 06, 8:25 PM

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