Number System

Natural Numbers (N)

{1,2,3,…}

Whole Numbers (W)

{0,1,2,3,…}

Integers (Z)

{…,−3,−2,−1,0,1,2,3,…}

Positive Integers (Z⁺)

{1,2,3,…}

Negative Integers (Z⁻)

{…,−3,−2,−1}

Even Numbers

Numbers divisible by 2

Odd Numbers

Numbers not divisible by 2

Prime Number

Has exactly 2 factors (1 & itself)

Smallest Prime Number

2

Only Even Prime Number

2

Composite Number

Has more than 2 factors

1

Neither prime nor composite

Co-prime Numbers

HCF = 1

Co-prime Numbers

Need not both be prime

Rational Number (Q)

p/q where p,q are integers & q≠0

Irrational Number

Cannot be expressed as p/q

Real Numbers (R)

Rational + Irrational Numbers

Complex Number

a+ib where i=√−1

Divisible Number

Divisible by numbers other than 1 & itself

Cyclic Number

Digits repeat cyclically on multiplication

Perfect Number

Sum of proper divisors = Number

Smallest Perfect Number

6

Perfect Numbers

6, 28, 496, 8128

Perfect Number Property

Sum of reciprocals of all factors = 2

π

3.141592653…

√2

1.414213562…

0

Neither positive nor negative