OBEB (ORTAK B\u00d6LENLER\u0130N EN B\u00dcY\u00dc\u011e\u00dc)
\nOBEB, iki veya daha \u00e7ok say\u0131y\u0131 ayn\u0131 anda b\u00f6lebilen en b\u00fcy\u00fck say\u0131d\u0131r. Verilen say\u0131lar\u0131n OBEB’ ini bulmak i\u00e7in, say\u0131lar asal \u00e7arpanlar\u0131na ayr\u0131l\u0131r ve ortak asal \u00e7arpanlar\u0131n en k\u00fc\u00e7\u00fck \u00fcsleri al\u0131n\u0131r.
\n1. Aralar\u0131nda asal iki say\u0131n\u0131n OBEB’ i 1′ dir. Yani, a ile b aralar\u0131nda asal iki say\u0131 ise,
\n(a, b)OBEB = 1 dir.
\n2. Ayn\u0131 zamanda, ikiden \u00e7ok say\u0131daki say\u0131lardan en az iki tanesi aralar\u0131nda asal ise, bu say\u0131lar\u0131n OBEB’ i 1′ dir. Yani, a, b, c, d, e say\u0131lar\u0131ndan a ile b aralar\u0131nda asal ise,
\n(a, b, c, d, e)OBEB = 1 dir.
\n3. \u0130ki veya daha fazla say\u0131n\u0131n ortak tam b\u00f6lenlerinin say\u0131s\u0131, OBEB’ inin b\u00f6lenlerinin say\u0131s\u0131na e\u015fittir.
\n4. Ard\u0131\u015f\u0131k iki sayma say\u0131s\u0131n\u0131n OBEB’ i 1′ dir. Yani, a ile b ard\u0131\u015f\u0131k iki sayma say\u0131s\u0131 olmak \u00fczere,
\n(a , b)OKEK = 1 dir.
\n\u00d6rnek 1:
\n18, 30, 42 say\u0131lar\u0131n\u0131n OBEB’ i ka\u00e7t\u0131r?
\n\u00c7\u00f6z\u00fcm:
\n1. Yol:<\/p>\n
18, 30 ve 42 say\u0131lar\u0131n\u0131n \u00fc\u00e7\u00fcn\u00fc birden b\u00f6len say\u0131lar 2 ve 3 t\u00fcr. Dolay\u0131s\u0131yla,
\n(18, 30, 42)OBEB = 2 . 3 = 6 d\u0131r.
\n2. Yol:
\n18 = 2.32
\n30 = 2.3.5
\n42 = 2.3.7
\nHer \u00fc\u00e7 say\u0131n\u0131n ortak asal \u00e7arpanlar\u0131n\u0131n en k\u00fc\u00e7\u00fck \u00fcsl\u00fcs\u00fc al\u0131nmal\u0131d\u0131r. Dolay\u0131s\u0131yla,
\n(18, 30, 42)OBEB = 2.3 = 6 d\u0131r.
\n\u00d6rnek 2:
\n100 ile 120 say\u0131lar\u0131n\u0131n OBEB’ i ka\u00e7t\u0131r?
\n\u00c7\u00f6z\u00fcm:
\n1. Yol:<\/p>\n
100 ile 120 say\u0131s\u0131n\u0131n ikisini birden b\u00f6len say\u0131lar\u0131 22 ile 5 dir. Dolay\u0131s\u0131yla,
\n(100, 120)OBEB = 22 . 5 = 4 . 5 = 20 dir.
\n2. Yol:
\n100 = 22.52
\n120 = 23.3.5
\nHer iki say\u0131n\u0131n ortak asal \u00e7arpanlar\u0131n\u0131n en k\u00fc\u00e7\u00fck \u00fcsl\u00fcs\u00fc al\u0131nmal\u0131d\u0131r. Dolay\u0131s\u0131yla,
\n(100, 120)OBEB = 22.5 = 20 dir.
\n\u00d6rnek 3:
\n6, 15 ve 29 say\u0131lar\u0131n\u0131n OBEB’ i ka\u00e7t\u0131r?
\n\u00c7\u00f6z\u00fcm:
\n\u0130kiden \u00e7ok say\u0131daki say\u0131lar\u0131n en az iki tanesi aralar\u0131nda asal ise, bu say\u0131lar\u0131n OBEB’ i 1 oldu\u011fundan, verilen say\u0131lardan 6 ile 29 say\u0131s\u0131 veya 15 ile 29 say\u0131s\u0131 aralar\u0131nda asal oldu\u011fu i\u00e7in
\n(6, 15, 29)OBEB = 1
\ndir.
\n\u00d6rnek 4:
\n100 ile 120 say\u0131lar\u0131n\u0131n ortak tam b\u00f6lenlerinin say\u0131s\u0131 ka\u00e7t\u0131r?
\n\u00c7\u00f6z\u00fcm:
\n(100, 120)OBEB = 22.51 = 20
\noldu\u011fundan, pozitif b\u00f6lenlerinin say\u0131s\u0131,
\n( 2 + 1) . ( 1 + 1 ) = 3 . 2 = 6
\nbulunur. Buradan, t\u00fcm b\u00f6lenlerin say\u0131s\u0131, pozitif b\u00f6lenlerin say\u0131s\u0131n\u0131n iki kat\u0131na e\u015fit oldu\u011fundan,
\n2 . 6 = 12 olur.
\n\u00d6rnek 5:
\nBoyutlar\u0131 9 cm, 12 cm, 15 cm olan dikd\u00f6rtgenler prizmas\u0131 bi\u00e7imindeki kutunun i\u00e7erisi, bo\u015f yer kalmayacak \u015fekilde en b\u00fcy\u00fck boyutlu k\u00fcplerle doldurulmak istenmektedir. Bu kutuya ka\u00e7 tane k\u00fcp yerle\u015ftirilebilir?
\n\u00c7\u00f6z\u00fcm:
\nKutu en b\u00fcy\u00fck boyutlu k\u00fcplerle doldurulmak istendi\u011finden, 9 cm, 12 cm, 15 cm say\u0131lar\u0131n\u0131n OBEB’ i bulunmal\u0131d\u0131r. Bu nedenle,
\n(9, 12, 15)OBEB = 3 t\u00fcr. B\u00f6ylece, en b\u00fcy\u00fck boyutlu k\u00fcp\u00fcn bir kenar\u0131 = 3 cm olur. Bir kenar\u0131 3 cm olacak \u015fekilde yerle\u015ftirilebilecek k\u00fcp say\u0131s\u0131,
\nK\u00fcp say\u0131s\u0131 = Kutunun hacmi \/ K\u00fcp\u00fcn hacmi = 9.12.15\/3.3.3 = 3.4.5 = 60
\ntane olur.
\n\u00d6rnek 6:
\nBoyutlar\u0131 24 m ve 60 m olan dikd\u00f6rtgen \u015feklindeki bir arsan\u0131n \u00e7evresine e\u015fit aral\u0131klarla en az say\u0131da ka\u00e7 a\u011fa\u00e7 dikilebilir?
\n\u00c7\u00f6z\u00fcm:
\n\u0130ki a\u011fac\u0131n aras\u0131ndaki uzakl\u0131k, dikd\u00f6rtgenin boyutlar\u0131n\u0131n OBEB’ i olur. Dolay\u0131s\u0131yla,
\n(24, 60)OBEB = 12
\nA\u011fa\u00e7 Say\u0131s\u0131 = \u00c7evre \/ 12 = 2 . (24 + 60) \/ 12 = 84 \/ 6 = 14
\ndir.<\/p>\n","protected":false},"excerpt":{"rendered":"
OBEB (ORTAK B\u00d6LENLER\u0130N EN B\u00dcY\u00dc\u011e\u00dc) OBEB, iki veya daha \u00e7ok say\u0131y\u0131 ayn\u0131 anda b\u00f6lebilen en b\u00fcy\u00fck say\u0131d\u0131r. Verilen say\u0131lar\u0131n OBEB’ ini bulmak i\u00e7in, say\u0131lar asal \u00e7arpanlar\u0131na ayr\u0131l\u0131r ve ortak asal \u00e7arpanlar\u0131n en k\u00fc\u00e7\u00fck \u00fcsleri al\u0131n\u0131r. 1. Aralar\u0131nda asal iki say\u0131n\u0131n OBEB’ i 1′ dir. Yani, a ile b aralar\u0131nda asal iki say\u0131 ise, (a, b)OBEB …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1404,1403],"tags":[7294,7295],"class_list":["post-3096","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-asal-carpanlar","tag-dikdortgenler-prizmasi"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3096","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/comments?post=3096"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3096\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3096"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3096"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3096"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}