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:**

**Positve 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 integer (1 and the integer itself, e.g. 2, 3, 5, 7, 11, 29 etc).**Coprime number**is pair of two positive integer 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 integer.

Example:6 is the LCM of 2 and 3

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

Example:GCD of 15 and 30 is 15

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

- Addition of two integer will be an integer (negative or positive).
- Subtraction of two integer will be an integer (negative or positive).
- Product of two integer will be an integer (negative or positive).
- Division of two integer 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