Classification of Numbers

Every number can be classified into one or more groups. So numbers can be classified as rational or irrational, natural, whole, or integer.

Natural Numbers

Natural Numbers are Counting Numbers.

For Example: 1, 2, 3, 4, 5 ……….

Even Numbers

Multiples of 2 are even numbers. Even Numbers are also Natural numbers

For Example: 2, 4, 6, 8, 10……………

Odd Numbers

Numbers which are not multiples of 2 are odd numbers. Odd numbers are also natural numbers

For Example: 1, 3, 5, 7 …

Prime Number

A prime number is a positive integer that has exactly two positive integer factors, 1 and itself. 

First few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37…

Co-prime

No common factors other than 1.
Example: 21 and 22 are coprime (the only common factor is 1)
• The factors of 21 are 1, 3, 7 and 21
• The factors of 22 are 1, 2, 11 and 22
Co-prime also called "relatively prime" or "mutually prime".

Twin Primes

Twin Primes are Successive odd numbers that are both Prime numbers.

For Example: (3, 5), (5, 7), (11, 13)...

Composite Number

Composite Numbers are values that can be factored into two or more values other than one (1) and itself.

First few composite numbers: 4,6,8,9,10,12,14,15,16,18,20,21………..

Whole Numbers

Whole Numbers include ALL natural numbers plus 0.

For Example: 0, 1, 2, 3…

Integers

Integers include ALL whole numbers as well as negative numbers

For Example: -3,-2,-1, 0, 1, 2, 3 …

Negative Integers:  … -5, -4, -3, -2, -1

Positive Integers: 1, 2, 3, 4, 5...

Non-Negative Integers: 0, 1, 2, 3, 4, 5...

Perfect numbers

Perfect number is a positive integer that is equal to the sum of its proper divisors.

Example 1: 6 (proper factors: 1, 2, 3) is a Perfect number because 1+2+3=6.

Example 2: 28 (proper factors: 1, 2, 4, 7, 14) is also a Perfect number, because 1+2+4+7+14=28.

Rational Numbers

Rational Numbers are any number that can be written as a fraction.

For Example: 3/5,-4/9     

Rational numbers can also be represented as decimals.

Example: 4/5 = 0.8, -27/4 =-6.75, 2/3= 0.66666 (6 is repeating)

Fractions

A fraction tells us how many parts of a whole we have.

For Example: 1/3 means 1 out of 3

Proper fraction

A fraction that is less than 1. The numerator is smaller than the denominator.

For Example: 2/3

Improper fraction

A fraction greater than or equal to 1.

For Example: 1/5, 2/5, 4/4

Mixed fraction

A whole number plus a proper fraction.

For Example: 2 1/3= 2+1/3

Irrational Numbers

An irrational number is a decimal that neither terminates (stops like 0.25) nor repeats (0.333333).

For Example: π= 3.14159265359…, sqrt (2) = 1.414213562… (these decimals continue)

If a number is rational, then it cannot be irrational

Real Numbers

Real Numbers includes both the rational and irrational numbers

For Example: 3, 5.68, -0.435, 5/6, sqrt (3), 176

Imaginary Numbers

A number that when squared gives a negative result. Represented by i.

i=sqrt (-1)
If you square any Real Number you always get a positive, or zero, result.

Example both 2×2, and (-2) × (-2) are equal to 4.

How can we square a number to get a negative result?

We "imagine" that we can …, which may seem impossible, is actually useful and can solve real problems.

Complex Numbers

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, that satisfies the equation i² = −1.

For Example: 3 + 2i, 27.2 - 11.05i