Szorozhatóság

Szorozhatóság, often translated as divisibility, is a fundamental concept in number theory. It concerns the relationship between two integers. An integer 'a' is said to be divisible by another integer 'b' if the division of 'a' by 'b' results in an integer with no remainder. In other words, if there exists an integer 'k' such that a = b * k, then 'a' is divisible by 'b'.

This relationship is often denoted using symbols. For example, if 'a' is divisible by 'b', it can be written as b | a. Conversely, if 'a' is not divisible by 'b', it is written as b <binary data, 1 bytes><binary data, 1 bytes> a. The integer 'b' is called a divisor or factor of 'a', and 'a' is called a multiple of 'b'.

The concept of divisibility is crucial for understanding prime numbers, composite numbers, greatest common divisors (GCD), and least common multiples (LCM). For instance, a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Divisibility rules are also practical shortcuts used to quickly determine if a number is divisible by small integers like 2, 3, 5, 9, and 10 without performing the actual division. These rules are based on patterns in the decimal representation of numbers. For example, a number is divisible by 2 if its last digit is even.