Deilatafla

Deilatafla er tafla yfir þætti talna. Tekið er dæmi um deilatöflu talnanna 1 til 1000. Með orðinu deilir er átt við sérhverja tölu, a, sem gengur upp í tiltekinni tölu, b, þar sem a og b eru heilar, pósitífar tölur. Sem dæmi eru deilar tölunnar 7 1 og 7 og deilar tölunnar 36 eru 1, 2, 3, 4, 6, 9, 12, 18 og 36. Talan 1 er deilir sérhverrar tölu og sérhver tala er deilir sjálfrar sín. Þeir deilar sem eru minni en talan sjálf kallast eiginlegir deilar. Sé summa eiginlegra deila minni en talan sjálf (dæmi: 10) kallast talan fátækleg tala (e.: deficient number). Ef summa eiginlegra deila er stærri en talan sjálf (dæmi: 36) kallast hún auðug tala (e.: abundant number). Sé summa eiginlegu deilanna jöfn tölunni sjálfri, kallast hún fullkomin tala (dæmi: 6). Í töflunni eru fátæklegar tölur merktar með - (mínus), auðugar með + (plús) og fullkomnar tölur eru feit- og skáletraðar. Aðeins ein tala hefur einn deili og ekki fleiri, það er talan 1 og kallast hún eining(in). Sumar tölur hafa nákvæmlega tvo deila, sem eru 1 og talan sjálf, þær tölur kallast frumtölur og eru óþáttanlegar. Allar aðrar tölur (heilar, pósitífar) kallast samsettar tölur og eru þáttanlegar. Til eru ýmsar deilireglur eða hjálparaðgerðir t.a. kanna hvort tala sé deilanleg með ákveðinni tölu.

Athugið: ν(n) er fjöldi af jákvæðum deilum n, þar með talið 1 og n sjálf. 
σ(n) er summan af öllum jákvæðum deilum n, þar með talið 1 og n sjálf. Tölur þar sem summa jákvæðra deila að frádregni tölunni sjálfri er minni en talan (σ(n)-n < n) eru merktar (σ(n)-n)-; tölur þar sem summa jákvæðra deila að frádregni tölunni sjálfri er stærri en talan (σ(n)-n > n) eru merktar (σ(n)-n)+; og þær þrjár tölur (undir 1000) sem eru fullkomnar (σ(n)-n = n) eru feit- og skáletraðar.

nDeilarν(n)σ(n)σ(n)-nnDeilarν(n)σ(n)σ(n)-n11110-5011,3,167,5014672171-21,2231-5021,2,251,5024756254-31,3241-5031,50325041-41,2,4373-5041,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,56,63,72,84,126,168,252,5042415601056+51,5261-5051,5,101,5054612107-61,2,3,641265061,2,11,22,23,46,253,5068864358-71,7281-5071,3,13,39,169,5076732225-81,2,4,84157-5081,2,4,127,254,5086896388-91,3,93134-5091,50925101-101,2,5,104188-5101,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510161296786+111,112121-5111,7,73,511459281-121,2,3,4,6,1262816+5121,2,4,8,16,32,64,128,256,512101023511-131,132141-5131,3,9,19,27,57,171,5138800287-141,2,7,1442410-5141,2,257,5144774260-151,3,5,154249-5151,5,103,5154624109-161,2,4,8,1653115-5161,2,3,4,6,12,43,86,129,172,258,516121232716+171,172181-5171,11,47,517457659-181,2,3,6,9,1863921+5181,2,7,14,37,74,259,5188912394-191,192201-5191,3,173,5194696177-201,2,4,5,10,2064222+5201,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520161260740+211,3,7,2143211-5211,52125221-221,2,11,2243614-5221,2,3,6,9,18,29,58,87,174,261,522121170648+231,232241-5231,52325241-241,2,3,4,6,8,12,2486036+5241,2,4,131,262,5246924400-251,5,253316-5251,3,5,7,15,21,25,35,75,105,175,52512992467-261,2,13,2644216-5261,2,263,5264792266-271,3,9,2744013-5271,17,31,527457649-281,2,4,7,14,28656285281,2,3,4,6,8,11,12,16,22,24,33,44,48,66,88,132,176,264,528201488960+291,292301-5291,23,529355324-301,2,3,5,6,10,15,3087242+5301,2,5,10,53,106,265,5308972442-311,312321-5311,3,9,59,177,5316780249-321,2,4,8,16,3266331-5321,2,4,7,14,19,28,38,76,133,266,532121120588+331,3,11,3344815-5331,13,41,533458855-341,2,17,3445420-5341,2,3,6,89,178,267,53481080546+351,5,7,3544813-5351,5,107,5354648113-361,2,3,4,6,9,12,18,3699155+5361,2,4,8,67,134,268,53681020484-371,372381-5371,3,179,5374720183-381,2,19,3846022-5381,2,269,5384810272-391,3,13,3945617-5391,7,11,49,77,5396684145-401,2,4,5,8,10,20,4089050+5401,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,5402416801140+411,412421-5411,54125421-421,2,3,6,7,14,21,4289654+5421,2,271,5424816274-431,432441-5431,3,181,5434728185-441,2,4,11,22,4468440-5441,2,4,8,16,17,32,34,68,136,272,544121134590+451,3,5,9,15,4567833-5451,5,109,5454660115-461,2,23,4647226-5461,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546161344798+471,472481-5471,54725481-481,2,3,4,6,8,12,16,24,481012476+5481,2,4,137,274,5486966418-491,7,493578-5491,3,9,61,183,5496806257-501,2,5,10,25,5069343-5501,2,5,10,11,22,25,50,55,110,275,550121116566+511,3,17,5147221-5511,19,29,551460049-521,2,4,13,26,5269846-5521,2,3,4,6,8,12,23,24,46,69,92,138,184,276,552161440888+531,532541-5531,7,79,553464087-541,2,3,6,9,18,27,54812066+5541,2,277,5544834280-551,5,11,5547217-5551,3,5,15,37,111,185,5558912357-561,2,4,7,8,14,28,56812064+5561,2,4,139,278,5566980424-571,3,19,5748023-5571,55725581-581,2,29,5849032-5581,2,3,6,9,18,31,62,93,186,279,558121248690+591,592601-5591,13,43,559461657-601,2,3,4,5,6,10,12,15,20,30,6012168108+5601,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560201488928+611,612621-5611,3,11,17,33,51,187,5618864303-621,2,31,6249634-5621,2,281,5624846284-631,3,7,9,21,63610441-5631,56325641-641,2,4,8,16,32,64712763-5641,2,3,4,6,12,47,94,141,188,282,564121344780+651,5,13,6548419-5651,5,113,5654684119-661,2,3,6,11,22,33,66814478+5661,2,283,5664852286-671,672681-5671,3,7,9,21,27,63,81,189,56710968401-681,2,4,17,34,68612658-5681,2,4,8,71,142,284,56881080512-691,3,23,6949627-5691,56925701-701,2,5,7,10,14,35,70814474+5701,2,3,5,6,10,15,19,30,38,57,95,114,190,285,570161440870+711,712721-5711,57125721-721,2,3,4,6,8,9,12,18,24,36,7212195123+5721,2,4,11,13,22,26,44,52,143,286,572121176604+731,732741-5731,3,191,5734768195-741,2,37,74411440-5741,2,7,14,41,82,287,57481008434-751,3,5,15,25,75612449-5751,5,23,25,115,5756744169-761,2,4,19,38,76614064-5761,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,144,192,288,5762116511075+771,7,11,7749619-5771,57725781-781,2,3,6,13,26,39,78816890+5781,2,17,34,289,5786921343-791,792801-5791,3,193,5794776197-801,2,4,5,8,10,16,20,40,8010186106+5801,2,4,5,10,20,29,58,116,145,290,580121260680+811,3,9,27,81512140-5811,7,83,581467291-821,2,41,82412644-5821,2,3,6,97,194,291,58281176594+831,832841-5831,11,53,583464865-841,2,3,4,6,7,12,14,21,28,42,8412224140+5841,2,4,8,73,146,292,58481110526-851,5,17,85410823-5851,3,5,9,13,15,39,45,65,117,195,585121092507-861,2,43,86413246-5861,2,293,5864882296-871,3,29,87412033-5871,58725881-881,2,4,8,11,22,44,88818092+5881,2,3,4,6,7,12,14,21,28,42,49,84,98,147,196,294,5881815961008+891,892901-5891,19,31,589464051-901,2,3,5,6,9,10,15,18,30,45,9012234144+5901,2,5,10,59,118,295,59081080490-911,7,13,91411221-5911,3,197,5914792201-921,2,4,23,46,92616876-5921,2,4,8,16,37,74,148,296,592101178586-931,3,31,93412835-5931,59325941-941,2,47,94414450-5941,2,3,6,9,11,18,22,27,33,54,66,99,198,297,594161440846+951,5,19,95412025-5951,5,7,17,35,85,119,5958864269-961,2,3,4,6,8,12,16,24,32,48,9612252156+5961,2,4,149,298,59661050454-971,972981-5971,3,199,5974800203-981,2,7,14,49,98617173-5981,2,13,23,26,46,299,59881008410-991,3,9,11,33,99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Flokkur:Algebra
Flokkur:Talnafræði