## 1. Tutoring: Even or odd? Integer numbers parity. 2. Examples of even and odd numbers. 3. The last digit of numbers. 4. Formal definition

### 1. Numbers' parity: even or odd?

- An integer is called an
**even number**if it is divisible by 2; in other words, an integer is called an even number if there is no remainder when dividing it by 2. - An integer is called an
**odd number**if it is not divisible by 2, in other words, if there is a remainder of 1 when dividing it by 2. - If a number is even then it is not an odd number.
- The property of an integer of being either even or odd is called
**parity**.

### 2. Examples of even and odd numbers:

- Even numbers: -14, 2, 0, 8, 56, and 127,388 (there is no remainder when divided by 2).
- Odd numbers: -13, 1, 5, 97, 19, and 127,387 (all leave a remainder of 1 when divided by 2).
- All the prime numbers except the number 2 are odd numbers.
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### 3. The numbers' last digit

- An integer number is even or odd depending on whether its last digit is even or odd.
- If the last digit of a number is 0, 2, 4, 6, or 8, then the number is even.
- If the last digit of a number is 1, 3, 5, 7, or 9, then the number is odd.

### 4. Formal definition of even and odd numbers:

- An even number, "a", can always be written as the product between 2 and some other integer, "k".
- The even number a = 2 × k
- As a result, an odd number, "b", since it leaves a remainder of 1 when divided by 2, can always be written as the product between 2 and some other integer, "k", plus 1.
- The odd number b = 2 × k + 1

### Did you know?

- In some countries the houses are numbered so that the ones on one side of the street have even numbers and the ones on the other side have odd numbers.