# GRE Arithmetic | Integers

There is a different type of numbers: natural number, real number, whole number, integers, etc. Integers are the numbers -1, -2, -3, -4, 1, 2, 5, 9, -10. Integers are either negative or positive (0 is the exception which is neither negative nor positive integer).

Let’s understand it by number line:

**Types of integers:**

**Positive integer**(e.g. 5, 8, 12, 29 etc).**Negative integer**(e.g. -5, -8, -12, -29 etc).**Even integers**(e.g. 4, 8, 12, 28, -28, -12, -8, -4 etc).**Odd integers**(e.g. 5, 9, 13, 29, -33. -31, -49 etc).- Neither positive nor negative integer is 0.
**Prime number**is an integer which is divisible by only two positive integers (1 and the integer itself, e.g. 2, 3, 5, 7, 11, 29, etc).**Coprime number**is pair of two positive integers which have 1 as a only common positive divisor.

What is least common multiple and greatest common divisor?

**Least common divisor (LCM):** It is the least common multiple of two positive integers.

Example:6 is the LCM of 2 and 3

**Greatest common divisor (GCD):** It is the greatest common factor (GCF) of two positive integers.

Example:GCD of 15 and 30 is 15

**Different type of operation can be performed on integers:**

- Addition of two integers will be an integer (negative or positive).
- Subtraction of two integers will be an integer (negative or positive).
- Product of two integers will be an integer (negative or positive).
- Division of two integers can be an integer or decimal (negative or positive).
- Square of an integer (negative or positive) will be a positive integer.
- Root of a positive integer can be an integer or decimal.

odd + odd = even odd - odd = even even + even = even even - even = even odd + even = odd odd - even = even Even - odd = odd odd * odd = odd even * even = even odd * even = even

**For example:**

3 + 3 = 6 (-3) + (-3) = -6 3 - 1 = 2 (-3) - (-1) = -2 4 + 4 = 8 (-4) + (-4) = -8 4 - 2 = 2 (-4) - (-2) = (-2) 3 + 4 = 7 (-3) + (-4) = (-7) 5 - 2 = 3 (-5) - (-2) = (-3) 5 - 3 = 2 (-5) - (-3) = (-2) 3 * 3 = 9 (-3) * (-3) = 9 4 * 4 = 16 (-4) * (-4) = 16 3 * 4 = 12 (-3) * (-4) = 12 √4 = 2 √2 = 1.41421... 6 / 2 = 3 (-6) / (-2) = 3 (-6) / 2 = -3 6 / (-2) = -3 5 / 2 = 2.5 (-5) / (-2) = 2.5 5 / (-2) = -2.5 (-5) / 2 = -2.5