{"id":85,"date":"2024-11-26T08:17:46","date_gmt":"2024-11-26T08:17:46","guid":{"rendered":"https:\/\/www.infomega.ro\/a10a\/?page_id=85"},"modified":"2024-11-28T22:41:51","modified_gmt":"2024-11-28T22:41:51","slug":"m2-l2-info-divizibilitate","status":"publish","type":"page","link":"https:\/\/www.infomega.ro\/a10a\/info\/m2-info\/m2-l2-info-divizibilitate\/","title":{"rendered":"M2 L2 Info Divizibilitate divizori proprii"},"content":{"rendered":"\n<p>Un num\u0103r \u00eentreg are <strong>divizori proprii<\/strong> \u0219i <strong>improprii<\/strong>. Divizorii <strong>improprii <\/strong>sunt <strong>1<\/strong> \u0219i num\u0103rul <strong>\u00eensu\u0219i<\/strong>. Toate numerele au divizori improprii. Divizorii <strong>proprii <\/strong>sunt toate celelalte numere la care num\u0103rul nostru <strong>se \u00eemparte f\u0103r\u0103 rest. <\/strong>Nu toate numerele au divizori proprii.<\/p>\n\n\n\n<p><strong>De exemplu<\/strong>, num\u0103rul  144 are divizorii:<\/p>\n\n\n\n<p>1,2,3,4,6,8,8,9,12,16,18,24,36,48,72,144 unde 1 \u0219i 144 sunt divizorii improprii.<\/p>\n\n\n\n<p>\u00cen programul de mai jos vom afi\u0219a divizorii proprii ce apar\u021bin unui num\u0103r \u00eentreg citit de la tastatur\u0103.<\/p>\n\n\n\n<figure class=\"wp-block-embed aligncenter is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Divizorii proprii ai unui num\u0103r \u00eentreg n citit de la tastatur\u0103.\" width=\"729\" height=\"410\" src=\"https:\/\/www.youtube.com\/embed\/nN5hxgoeyDE?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><figcaption class=\"wp-element-caption\">video 1 divizori proprii<\/figcaption><\/figure>\n\n\n\n<p>Cod:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>#include &lt;iostream>\n\nusing namespace std;\n\nint main()\n{\n    int n,d=2;\n    do{\n        cout &lt;&lt; \"dati nr. pozitiv \";\n        cin >> n;\n    }while(n&lt;=0);\n    while(d&lt;=n\/2){\n        if(n%d==0){\n            cout &lt;&lt; d &lt;&lt;\" \";\n        }\n        d++;\n    }\n    return 0;\n}<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">Explicarea codului:<\/h2>\n\n\n\n<p>Acest program determin\u0103 \u0219i afi\u0219eaz\u0103 <strong>to\u021bi divizorii proprii<\/strong> ai unui num\u0103r pozitiv introdus de la tastatur\u0103. Iat\u0103 o explica\u021bie detaliat\u0103 pentru fiecare parte a programului:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">1. <strong>Biblioteca \u0219i spa\u021biul de nume<\/strong>:<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>#include &lt;iostream>\nusing namespace std;<\/code><\/pre>\n\n\n\n<p><strong><code>#include &lt;iostream><\/code><\/strong>: Este utilizat\u0103 pentru func\u021bii de intrare \u0219i ie\u0219ire precum <code>cin<\/code> (pentru citire de la tastatur\u0103) \u0219i <code>cout<\/code> (pentru afi\u0219are pe ecran).<\/p>\n\n\n\n<p><strong><code>using namespace std;<\/code><\/strong>: Permite utilizarea func\u021biilor din biblioteca standard f\u0103r\u0103 a scrie <code>std::<\/code> \u00eenaintea lor.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">2. <strong>Func\u021bia principal\u0103<\/strong>:<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>int main() {\n    int n, d = 2;<\/code><\/pre>\n\n\n\n<p><strong><code>int n<\/code><\/strong>: Variabila <code>n<\/code> este utilizat\u0103 pentru a stoca num\u0103rul introdus de utilizator.<\/p>\n\n\n\n<p><strong><code>int d = 2<\/code><\/strong>: Variabila <code>d<\/code> reprezint\u0103 un posibil divizor \u0219i este ini\u021bializat\u0103 cu 2, deoarece divizorii proprii nu includ 1 (care este implicit) \u0219i num\u0103rul \u00eensu\u0219i.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">3. <strong>Citirea unui num\u0103r pozitiv<\/strong>:<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>do {\n    cout &lt;&lt; \"dati nr. pozitiv \";\n    cin >> n;\n} while (n &lt;= 0);<\/code><\/pre>\n\n\n\n<p><strong>Func\u021bionalitate<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Blocheaz\u0103 execu\u021bia programului p\u00e2n\u0103 c\u00e2nd utilizatorul introduce un <strong>num\u0103r strict pozitiv<\/strong>.<\/li>\n\n\n\n<li>Bucla <code>do-while<\/code>:\n<ul class=\"wp-block-list\">\n<li>Afi\u0219eaz\u0103 mesajul <code>dati nr. pozitiv<\/code> \u0219i cite\u0219te valoarea introdus\u0103 \u00een <code>n<\/code>.<\/li>\n\n\n\n<li>Dac\u0103 valoarea lui <code>n<\/code> este mai mic\u0103 sau egal\u0103 cu 0, bucla se repet\u0103.<\/li>\n\n\n\n<li>Dac\u0103 <code>n > 0<\/code>, bucla se opre\u0219te \u0219i programul continu\u0103.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>Exemplu de comportament<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Utilizatorul introduce <code>-5<\/code>: <code>Num\u0103rul trebuie s\u0103 fie pozitiv<\/code>.<\/li>\n\n\n\n<li>Utilizatorul introduce <code>0<\/code>: <code>Num\u0103rul trebuie s\u0103 fie pozitiv<\/code>.<\/li>\n\n\n\n<li>Utilizatorul introduce <code>12<\/code>: Bucla se opre\u0219te.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">4. <strong>Determinarea divizorilor proprii<\/strong>:<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>while (d &lt;= n \/ 2) {\n    if (n % d == 0) {\n        cout &lt;&lt; d &lt;&lt; \" \";\n    }\n    d++;\n}<\/code><\/pre>\n\n\n\n<p><strong>Bucla <code>while<\/code><\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Aceast\u0103 bucl\u0103 iterativ\u0103 verific\u0103 fiecare posibil divizor <code>d<\/code> de la 2 p\u00e2n\u0103 la <code>n \/ 2<\/code>. Nu este nevoie s\u0103 verific\u0103m valori mai mari dec\u00e2t <code>n \/ 2<\/code>, deoarece un num\u0103r nu are divizori proprii mai mari dec\u00e2t jum\u0103tatea sa.<\/li>\n<\/ul>\n\n\n\n<p><strong>Condi\u021bia <code>if (n % d == 0)<\/code><\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Testeaz\u0103 dac\u0103 <code>d<\/code> este un divizor al lui <code>n<\/code>:\n<ul class=\"wp-block-list\">\n<li>Dac\u0103 restul \u00eemp\u0103r\u021birii lui <code>n<\/code> la <code>d<\/code> este 0 (<code>n % d == 0<\/code>), \u00eenseamn\u0103 c\u0103 <code>d<\/code> divide exact <code>n<\/code>.<\/li>\n\n\n\n<li>\u00cen acest caz, <code>d<\/code> este afi\u0219at pe ecran.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>Incrementul <code>d++<\/code><\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cre\u0219te valoarea lui <code>d<\/code> cu 1 la fiecare itera\u021bie, pentru a verifica urm\u0103torul posibil divizor.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">5. <strong>Ie\u0219irea din program<\/strong>:<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>return 0;<\/code><\/pre>\n\n\n\n<p>Marcheaz\u0103 \u00eencheierea programului.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Exemplu de rulare:<\/h2>\n\n\n\n<p><strong>Caz 1: Num\u0103r pozitiv care nu este prim (are divizori proprii)<\/strong>:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>dati nr. pozitiv: -3\ndati nr. pozitiv: 0\ndati nr. pozitiv: 12\n2 3 4 6 <\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Caz 2: Num\u0103r prim (nu are divizori proprii)<\/strong>:<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>dati nr. pozitiv: 7<\/code><\/pre>\n\n\n\n<p>Nu afi\u0219eaz\u0103 nimic, deoarece un num\u0103r prim nu are divizori proprii (divizorii s\u0103i sunt doar 1 \u0219i el \u00eensu\u0219i).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Comportament general:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Solicit\u0103 utilizatorului s\u0103 introduc\u0103 un <strong>num\u0103r strict pozitiv<\/strong>.<\/li>\n\n\n\n<li>Detecteaz\u0103 \u0219i afi\u0219eaz\u0103 to\u021bi <strong>divizorii proprii<\/strong> ai acelui num\u0103r.<\/li>\n\n\n\n<li>Ignor\u0103 numerele negative, zero, sau cazurile unde num\u0103rul nu are divizori proprii.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Observa\u021bii:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Bucla <code>do-while<\/code><\/strong> este util\u0103 pentru validarea intr\u0103rii utilizatorului.<\/li>\n\n\n\n<li><strong>Bucla <code>while<\/code> \u0219i condi\u021bia <code>if<\/code><\/strong> sunt esen\u021biale pentru identificarea divizorilor proprii.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Tem\u0103:<\/h2>\n\n\n\n<p>S\u0103 se modifice programul de mai sus pentru a afi\u0219a dac\u0103 un num\u0103r \u00eentreg citit de le tastatur\u0103 este prim.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Un num\u0103r \u00eentreg are divizori proprii \u0219i improprii. Divizorii improprii sunt 1 \u0219i num\u0103rul \u00eensu\u0219i. Toate numerele au divizori improprii. Divizorii proprii sunt toate celelalte numere la care num\u0103rul nostru se \u00eemparte f\u0103r\u0103 rest. Nu toate numerele au divizori proprii. De exemplu, num\u0103rul 144 are divizorii: 1,2,3,4,6,8,8,9,12,16,18,24,36,48,72,144 unde 1 \u0219i 144 sunt divizorii improprii. \u00cen [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":37,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_FSMCFIC_featured_image_caption":"","_FSMCFIC_featured_image_nocaption":"","_FSMCFIC_featured_image_hide":"","footnotes":""},"class_list":["post-85","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>M2 L2 Info Divizibilitate divizori proprii - Clasa a X-a InfoMega<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.infomega.ro\/a10a\/info\/m2-info\/m2-l2-info-divizibilitate\/\" \/>\n<meta property=\"og:locale\" content=\"ro_RO\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"M2 L2 Info Divizibilitate divizori proprii - Clasa a X-a InfoMega\" \/>\n<meta property=\"og:description\" content=\"Un num\u0103r \u00eentreg are divizori proprii \u0219i improprii. Divizorii improprii sunt 1 \u0219i num\u0103rul \u00eensu\u0219i. Toate numerele au divizori improprii. Divizorii proprii sunt toate celelalte numere la care num\u0103rul nostru se \u00eemparte f\u0103r\u0103 rest. Nu toate numerele au divizori proprii. De exemplu, num\u0103rul 144 are divizorii: 1,2,3,4,6,8,8,9,12,16,18,24,36,48,72,144 unde 1 \u0219i 144 sunt divizorii improprii. \u00cen [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.infomega.ro\/a10a\/info\/m2-info\/m2-l2-info-divizibilitate\/\" \/>\n<meta property=\"og:site_name\" content=\"Clasa a X-a InfoMega\" \/>\n<meta property=\"article:modified_time\" content=\"2024-11-28T22:41:51+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Timp estimat pentru citire\" \/>\n\t<meta name=\"twitter:data1\" content=\"3 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/info\\\/m2-info\\\/m2-l2-info-divizibilitate\\\/\",\"url\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/info\\\/m2-info\\\/m2-l2-info-divizibilitate\\\/\",\"name\":\"M2 L2 Info Divizibilitate divizori proprii - Clasa a X-a InfoMega\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/#website\"},\"datePublished\":\"2024-11-26T08:17:46+00:00\",\"dateModified\":\"2024-11-28T22:41:51+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/info\\\/m2-info\\\/m2-l2-info-divizibilitate\\\/#breadcrumb\"},\"inLanguage\":\"ro-RO\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/info\\\/m2-info\\\/m2-l2-info-divizibilitate\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/info\\\/m2-info\\\/m2-l2-info-divizibilitate\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Prima pagin\u0103\",\"item\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Info\",\"item\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/info\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"M2 Info\",\"item\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/info\\\/m2-info\\\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"M2 L2 Info Divizibilitate divizori proprii\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/#website\",\"url\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/\",\"name\":\"Clasa a X-a InfoMega\",\"description\":\"Informa\u021bia a\u0219a cum o po\u021bi imagina\",\"publisher\":{\"@id\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/#\\\/schema\\\/person\\\/9694de2962f527a4ed763694fd74245e\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"ro-RO\"},{\"@type\":[\"Person\",\"Organization\"],\"@id\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/#\\\/schema\\\/person\\\/9694de2962f527a4ed763694fd74245e\",\"name\":\"2nf0\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"ro-RO\",\"@id\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2024\\\/11\\\/150colorchanger.png\",\"url\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2024\\\/11\\\/150colorchanger.png\",\"contentUrl\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2024\\\/11\\\/150colorchanger.png\",\"width\":150,\"height\":150,\"caption\":\"2nf0\"},\"logo\":{\"@id\":\"https:\\\/\\\/www.infomega.ro\\\/a10a\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2024\\\/11\\\/150colorchanger.png\"},\"sameAs\":[\"https:\\\/\\\/www.infomega.ro\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"M2 L2 Info Divizibilitate divizori proprii - Clasa a X-a InfoMega","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.infomega.ro\/a10a\/info\/m2-info\/m2-l2-info-divizibilitate\/","og_locale":"ro_RO","og_type":"article","og_title":"M2 L2 Info Divizibilitate divizori proprii - Clasa a X-a InfoMega","og_description":"Un num\u0103r \u00eentreg are divizori proprii \u0219i improprii. Divizorii improprii sunt 1 \u0219i num\u0103rul \u00eensu\u0219i. Toate numerele au divizori improprii. Divizorii proprii sunt toate celelalte numere la care num\u0103rul nostru se \u00eemparte f\u0103r\u0103 rest. Nu toate numerele au divizori proprii. 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