### Theory:

The closure property of integers states that while performing any operation such as (

**addition**,**subtraction**,**multiplication**) with two or more integers, the result of the operation is also an integer.The result of addition, subtraction and multiplication of any two integers is also an integer.

If \(a\) and \(b\) are two integers then:

(\(a + b\)) is also an integer.

(\(a - b\)) is also an integer.

(\(a × b\)) is also an integer.

Example:

\(3\) and \(4\) are two integers, then (\(3 + 4\)) \(= 7\) is also an integer.

\(3\) and \(4\) are two integers, then (\(3 - 4\)) \(= -1\) is also an integer.

\(3\) and \(4\) are two integers, then (\(3 × 4\)) \(= 12\) is also an integer.

Important!

The result of the division of any two integers is not always an integer. If \(a\) and \(b\) are two integers, then (\(a ÷ b\)) is not always an integer.

Example:

(\(12 ÷ 4\)) \(= 3\) is an integer.

(\(12 ÷ 5\)) \(= 12/5\) is not an integer.

(\(12 ÷ 5\)) \(= 12/5\) is not an integer.