# Integers

### Properties of Integers

###### Properties of Integers

Integers is the set of negative, zero and positive numbers, with no decimal or fraction part.

Example:

..., −4, −3, −2, −1, 0, 1, 2, 3, 4, ...

The following groups of numbers are included in integers:

1. Whole number

Whole number is integers that are not negative.

Example: 0, 1, 2, 3, 4, ...

2. Natural number

Natural number is the positive numbers of integers.

Example: 1, 2, 3, 4, ...

3. Even number

Even number is integers that divisible by two.

Example: ..., −6, −4, −2, 0, 2, 4, 6, ...

4. Odd number

Odd number is integers that have a remainder when divided by two.

Example: ..., −5, −3, −1, 1, 3, 5, ...

5. Prime number

Prime number is natural number that has two factors, 1 and and the number itself.

Example: 2, 3, 5, 7, 11, 13, 17, 19, 23, ...

6. Composite number

Composite number is natural number that has more than two factors.

Example: 4, 6, 8, 9, 10, 12, 14, …

Quadratic number is natural number resulting from the square of a number.

Example: 1, 4, 9, 16, 25, 36, 49, …

8. Cubic number

Cubic number is natural number resulting from the cube of a number.

Example: 1, 8, 27, 64, 125, 216, 343, …

##### Properties of integers

1. Closure property

The operation of addition, subtraction and multiplication on integers will resulting an integers as well.

If a, b and c are integers, so the result of a + b × c is integers as well.

a + b × c ∈ Z

2. Commutative property of addition and multiplication

a + b = b + a

a × b = b × a

3. Associative property of addition and multiplication

(a + b) + c = a + (b + c)

(a × b) × c = a × (b × c)

4. Distributive property

a × (b + c) = (a × b) + (a × c)

a × (b − c) = (a × b) − (a × c)

5. Identity property

a + 0 = a

a × 1 = a