oszthatóság

Divisibility is a fundamental concept in number theory. An integer 'a' is said to be divisible by another integer 'b' if there exists an integer 'c' such that a = b * c. This means that when 'a' is divided by 'b', the remainder is zero. The number 'b' is called a divisor or factor of 'a', and 'a' is called a multiple of 'b'. For example, 12 is divisible by 3 because 12 = 3 * 4. Here, 3 is a divisor of 12, and 12 is a multiple of 3.

If 'a' is divisible by 'b', we often denote this relationship using the notation b | a. Conversely, if 'a' is not divisible by 'b', we write b <binary data, 1 bytes><binary data, 1 bytes> a. Divisibility is a transitive relation: if a | b and b | c, then a | c. It is also reflexive: a | a for any integer 'a'.

There are several divisibility rules that can help determine if a number is divisible by another without performing long division. For instance, a number is divisible by 2 if its last digit is even. A number is divisible by 3 if the sum of its digits is divisible by 3. A number is divisible by 5 if its last digit is 0 or 5. Understanding divisibility is crucial for concepts like prime factorization, greatest common divisor (GCD), and least common multiple (LCM).