Bölme Bölünebilme Konusu
Bölme Bölünebilme
A) Bölme
a, b, c, d, ve k birer doğal sayı, b ≠ 0 olmak üzere,
Bölme işleminde;
a : bölünen
b : bölen
c : bölüm
k : kalan ise
a = b.c + k biçiminde gösterilir.
Bir bölme işleminde;
- k < b dir.
- k = 0 ise a sayısı b sayısına tam olarak bölünür.
- Kalan bölümden küçük ise bölen ile bölümün yerlerinin değiştirilmesi kalanı değiştirmez.
C) Bir Doğal Sayının Tam Bölenleri
1. Bir Doğal Sayının Çarpanlarına Ayrılması
Örnek:
120 sayısının asal çarpanlarını bulalım. Çözüm: 120=23.3.5 tir.
120 nin asal çarpanları 2, 3, ve 5 tir.
2. Bir Doğal Sayının Tam Bölenlerinin Sayısı
Bir A sayısının asal çarpanlarına ayrılmış şekli;
A = xa.yb.zc olsun.
- A sayısının pozitif tam bölenlerinin sayısı = (a + 1)(b + 1)(c + 1) dir.
- A sayısının tam sayı bölenlerinin sayısı = 2.(a + 1)(b + 1)(c + 1) dir.
- A sayısının tam sayı bölenlerinin toplamı sıfırdır.
- A sayısının asal bölenlerinin sayısı 3 tür. Bunlar x, y, z dir.
B) Bölünebilme Kuralları
Burada sırasıyla 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ve 25 ile
bölünebilme kuralları verilmiştir.
bölünebilme kuralları verilmiştir.
2 ile bölünebilme : Her çift sayı 2 ile tam bölünür. Tek sayılar 2 ile tam bölünemeyip 1 kalanını verir.
3 ile bölünebilme : Rakamlarının toplamı 3 ün katı olan sayı 3 ile tam bölünür. Kalan, rakamlar toplamının 3 ile bölümünden kalana eşittir.
4 ile bölünebilme : Bir sayının son iki basamağı 4 ün katı ise bu sayı 4 e tam bölünür. Kalan son iki basamağında belirtilen sayının 4 ile bölümüne eşittir.
5 ile bölünebilme : Bir sayının son rakamında 0 veya 5 bulunuyorsa o sayı 5 ile tam bölünür. Aksi halde kalan son basamağın 5 ile bölümünden kalana eşittir.
6 ile bölünebilme : Eğer bir sayı 2 ve 3 e tam bölünüyorsa 6 ya da tam bölünür.
7 ile bölünebilme : 1, 3 ve 2 sayıları bir sayının sırasıyla birler, onlar ve yüzler basamağıyla sırayla çarpılır. Çıkan üçlü grupların toplamlarının farkı, o sayının 7 ile bölümünden kalana eşittir.
8 ile bölünebilme : Bir sayının son üç basamağının oluşturduğu sayı 8 ile tam bölünüyorsa o sayı 8 ile tam bölünür. Kalan o sayının son üç basamağının oluşturan sayının 8 ile bölümünden kalana eşittir.
9 ile bölünebilme : Rakamlarının toplamı 9 un katı olan sayı 9 ile tam bölünür. Kalan, rakamlar toplamının 9ile bölümünden kalana eşittir.
10 ile bölünebilme : Bir sayının son rakamı 0 ise o sayı 10 ile tam bölünür. Değil ise o sayının 10 ile bölümünden kalan, o sayının son (birler) basamağındaki rakama eşittir.
11ile bölünebilme : abcdef gibi bir sayının 11 ile bölümünden kalanı bulmak için birler basamağından itibaren birer atlanarak toplanır. Çıkan iki ayrı değerin farkının 11 ile bölümünden kalan, sayının 11 ile bölümünden kalana eşittir.
25 ile bölünebilme : Bir sayının son iki basamağındaki sayı 25 in katıysa o sayı 25 ile tam bölünür. Aksi durumda son iki basamağından oluşan sayının 25 ile bölümünden kalan, o sayının 25 ile bölümünden kalana eşittir.
2 ve 3 ile bölünebilen sayılar 6 ile, Uyarı: Aralarında asal sayılara tma bölünebilen bir sayı bu sayıların çarpımına da tam bölünür.
2 ve 5 ile bölünebilen sayılar 10 ile,
3 ve 4 ile bölünebilen sayılar 12 ile,
3 ve 5 ile bölünebilen sayılar 15 ile,
2 ve 9 ile bölünebilen sayılar 18 ile,
4 ve 5 ile bölünebilen sayılar 20 ile,
2 ve 11 ile bölünebilen sayılar 22 ile,
3 ve 8 ile bölünebilen sayılar 24 ile,
4 ve 9 ile bölünebilen sayılar 36 ile,
5 ve 9 ile bölünebilen sayılar 45 ile,
3 ve 4 ile bölünebilen sayılar 12 ile,
3 ve 5 ile bölünebilen sayılar 15 ile,
2 ve 9 ile bölünebilen sayılar 18 ile,
4 ve 5 ile bölünebilen sayılar 20 ile,
2 ve 11 ile bölünebilen sayılar 22 ile,
3 ve 8 ile bölünebilen sayılar 24 ile,
4 ve 9 ile bölünebilen sayılar 36 ile,
5 ve 9 ile bölünebilen sayılar 45 ile,
Soru:
Cevap:
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)
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)
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)
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Soru:
Cevap:
Bölme Bölünebilme ile İlgili Yazılar
Bölme Bölünebilme ve Asal Sayılar Videolu Anlatım
Bölme Bölünebilme ve Asal Sayılar videolu anlatımdır. Bölme Bölünebilme ve Asal Sayılar konusunun yıllara göre çıkmış soru dağılımları aşağıdaki tabloda verilmiştir. Konuyla ilgili daha ayrıntılı bilgiye ve videolu konu anlatımımıza erişmek için devamını oku linkine tıklayınız.