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Öğretmen, öğrencilerin zor sorulara hazırlıklı olmaları gerektiğini vurgulamaktadır."]},"endTime":2387,"title":"Asal Sayılar Konusu Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Asal Sayılar Konusuna Giriş","list":{"type":"unordered","items":["Akar sayılarca bir kampına son hızla devam ediliyor ve fasiküldeki asal sayılar konusunun ikinci videosu sunuluyor.","Asal sayılar konusu zor görünse de aslında çok zevkli bir konu olarak vurgulanıyor."]},"beginTime":0,"endTime":22,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=0&ask_summarization=1"},{"index":1,"title":"İlk Asal Sayı Sorusu","list":{"type":"unordered","items":["İlk soruda x bir pozitif tam sayı olmak üzere, verilen ifadenin bir asal sayının küpüne eşit olduğu belirtiliyor.","3000 sayısının asal çarpanlarına ayrılmış hali 3 × 2³ × 5³ olarak bulunuyor.","x sayısının pozitif tam sayı bölenlerinin sayısı 8 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× 37² × 30 olarak bulunuyor.","Pozitif bölen sayısı 48 olduğu için tam sayı bölenlerinin sayısı 96 olarak hesaplanıyor."]},"beginTime":309,"endTime":468,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=309&ask_summarization=1"},{"index":4,"title":"İki Basamaklı Sayıların Pozitif Bölenleri","list":{"type":"unordered","items":["Rakamları birbirinden farklı iki basamaklı ab doğal sayısının pozitif bölenlerinin sayısı altıdır.","Bir sayının pozitif bölen sayısını bulmak için üsleri bir artırarak çarpılır.","Pozitif bölen sayısı altı olan sayılar iki asal sayının çarpımı olabilir ve üsler 1'e 2 veya 2'ye 1 olmalıdır."]},"beginTime":470,"endTime":626,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=470&ask_summarization=1"},{"index":5,"title":"En Büyük ve En Küçük Değerlerin Bulunması","list":{"type":"unordered","items":["En büyük iki basamaklı sayı 98'dir (2×49) çünkü rakamları farklı ve pozitif bölen sayısı altıdır.","En küçük iki basamaklı sayı 12'dir (2²×3) çünkü rakamları farklı ve pozitif bölen sayısı altıdır.","En büyük ve en küçük değerlerin toplamı 110'dur."]},"beginTime":626,"endTime":742,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=626&ask_summarization=1"},{"index":6,"title":"Gundidaş Sayılar","list":{"type":"unordered","items":["Asal çarpanları aynı olan iki doğal sayının pozitif bölenleri sayısı birbirine eşitse bu iki sayıya gundidaş sayılar denir.","12 ve 18 gundidaş sayılardır çünkü asal çarpanları aynı (2×3) ve pozitif bölen sayıları eşittir.","İki sayının gundidaş olması için hem asal çarpanları aynı olmalı hem de üsleri aynı olmalıdır."]},"beginTime":742,"endTime":832,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=742&ask_summarization=1"},{"index":7,"title":"270 ile Gundidaş Sayı","list":{"type":"unordered","items":["270 sayısının asal çarpanları 2, 3 ve 5'tir.","270 ile gundidaş olan en küçük sayı 120'dir (2³×3×5) çünkü asal çarpanları aynı ve pozitif bölen sayıları eşittir.","120 sayısının rakamları toplamı 3'tür."]},"beginTime":832,"endTime":932,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=832&ask_summarization=1"},{"index":8,"title":"İki Basamaklı Sayı Problemi","list":{"type":"unordered","items":["İki basamaklı ab doğal sayısı için dört maddeden üçünün yanlış ve üçünün doğru olduğu biliniyor.","Asal sayılarla ilgili sorularda asal sayıları küçükten büyüğe doğru sırayla yazmak faydalıdır.","Problemin çözümünde asal bölenlerin sayısı, 21'e kalansız bölünebilme, 33 katının asal bölenlerin sayısı ve 28 katının asal bölenlerin sayısı gibi bilgiler kullanılır."]},"beginTime":932,"endTime":1066,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=932&ask_summarization=1"},{"index":9,"title":"Asal Sayıların Çarpımı Problemi","list":{"type":"unordered","items":["AB'nin en küçük değerini bulmak için, AB'nin iki asal sayının çarpımı şeklinde yazılacağı belirtiliyor.","33 katının asal bölenlerinin sayısı 4 olduğundan, p ve q'dan biri 3 veya 11 olamaz.","28 katının asal bölenlerinin sayısı 4 olduğundan, p ve q'dan biri 2 veya 7 olamaz.","P ve q'ye en az değer olarak 5 ve 13 seçildiğinde, AB'nin en küçük değeri 65 olur ve a+b toplamı en az 11 olur."]},"beginTime":1068,"endTime":1248,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=1068&ask_summarization=1"},{"index":10,"title":"Rakamları Asal Sayılardan Oluşan İki Basamaklı Sayılar","list":{"type":"unordered","items":["Rakamları asal sayılardan oluşan iki basamaklı doğal sayılar için, rakam olan asal sayılar 2, 3, 5 ve 7'dir.","Bu asal rakamlarla oluşturulan iki basamaklı sayılar: 23, 32, 25, 52, 27, 72, 35, 53, 37, 73, 57, 75'tir.","Rakamları farklı olmayan sayılar da dahil edildiğinde, toplam 16 farklı iki basamaklı doğal sayı vardır."]},"beginTime":1248,"endTime":1350,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=1248&ask_summarization=1"},{"index":11,"title":"Kareli Asal Sayılar","list":{"type":"unordered","items":["İki basamaklı ab doğal sayısı, a doğal sayısı asal iken a²+b² ifadesi de bir asal sayı oluyorsa \"kareli asal\" olarak adlandırılır.","Kareli asal sayılar için hem ab sayısı hem de a²+b² ifadesi asal olmalıdır.","İki basamaklı asal sayılar: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97'dir."]},"beginTime":1350,"endTime":1439,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=1350&ask_summarization=1"},{"index":12,"title":"Asal Sayılar ve Kare Toplamı","list":{"type":"unordered","items":["Bir asal sayının kareleri toplamı (a² + b²) asal sayı olabilmesi için hem a hem b tek sayı olamaz çünkü tek sayıların kareleri toplamı çift olur ve çift sayılar asal değildir.","11, 23, 41, 61 ve 83 sayıları, bir asal sayının kareleri toplamı asal sayı olan iki basamaklı asal sayılardır.","Bu sorunun cevabı Bursa'dır."]},"beginTime":1441,"endTime":1688,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=1441&ask_summarization=1"},{"index":13,"title":"Asil Asal Sayılar","list":{"type":"unordered","items":["Bir tam sayının karesinin bir fazlasına eşit olan asal sayılara asil asal sayılar denir.","İki basamaklı asil asal sayılar 17 ve 37'dir.","Bu iki basamaklı asil asal sayıların toplamı 54'tür."]},"beginTime":1688,"endTime":1787,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=1688&ask_summarization=1"},{"index":14,"title":"Asal Bölenler Arasındaki Fark","list":{"type":"unordered","items":["Bir sayının en büyük ve en küçük asal bölenleri arasındaki fark 1 ise, o sayı 2 ve 3 asal sayılarının çarpımıdır.","İki basamaklı doğal sayının en küçük asal böleni 2, en büyük asal böleni 3 ve aralarındaki fark 1 ise, bu sayı 96'dır.","96 sayısının asal bölenleri sadece 2 ve 3'tür."]},"beginTime":1791,"endTime":1883,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=1791&ask_summarization=1"},{"index":15,"title":"Asal Bölenlerin Toplamı","list":{"type":"unordered","items":["Bir sayının asal bölenlerinin toplamı 16 ise, o sayının asal bölenleri 5 ve 11, 3 ve 13 veya 2, 3 ve 11 olabilir.","Asal bölenlerinin toplamı 16 olan en küçük üç basamaklı sayı 55'tir.","Asal bölenlerinin toplamı 16 olan en büyük iki basamaklı sayı 66'dır ve bunların toplamı 883'tür."]},"beginTime":1883,"endTime":2190,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=1883&ask_summarization=1"},{"index":16,"title":"Karakteristik Kavramı","list":{"type":"unordered","items":["Bir doğal sayının en büyük asal çarpanı o sayının karakteristiği olarak adlandırılır.","Karakteristiği 7 olan en küçük üç basamaklı doğal sayı 105'tir.","Karakteristiği 3 olan en büyük iki basamaklı doğal sayı 96'dır ve bunların farkı 9'dur."]},"beginTime":2190,"endTime":2341,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=2190&ask_summarization=1"},{"index":17,"title":"Zor Soruların Önemi","list":{"type":"unordered","items":["Asal sayılarla ilgili zor sorular da sınavlarda gelebilir, bu nedenle her türlü senaryoya hazırlıklı olmak gerekir.","Zor soruların mantığını kavramak algıları açar ve sınavda avantaj sağlar."]},"beginTime":2341,"endTime":2385,"href":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=2341&ask_summarization=1"}],"linkTemplate":"/video/preview/13007368966544447763?parent-reqid=1768932572517510-7648588384801646237-balancer-l7leveler-kubr-yp-vla-51-BAL&text=Prime+Numbers&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Prime Numbers | Video 2 | 2026 | KPSS - DGS - AGS - ALES | Mathematics | Numbers and Algebra Camp","related_orig_text":"Prime Numbers","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Prime 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