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
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