Divisibility is a concept in mathematics that refers to the ability of one integer to be evenly divided by another integer without a remainder. The properties of divisibility are as follows:

Reflexivity: Every integer is divisible by 1 and itself.

Transitivity: If a is divisible by b, and b is divisible by c, then a is divisible by c.

Antisymmetric: If a is divisible by b and b is divisible by a, then a and b are equal.

Division Algorithm: For any integer a and positive integer b, there exists a unique integer q and a nonnegative integer r such that a = b * q + r,

Additivity: If a is divisible by b, and c is divisible by d, then a + c is divisible by b + d.

Multiplicativity: If a is divisible by b, and c is divisible by d, then a * c is divisible by b * d.

These properties allow us to determine if one integer is divisible by another and to simplify arithmetic operations involving multiple integers. Divisibility is a fundamental concept in number theory and plays a key role in many mathematical problems and applications.