### Number System,Theory of divisibility,Highest power in a factorial

## FORMULAE

# Number System

Real numbers are of two types: Decimal and Integers. The Integers have no decimal values like 0.33, 0.45; Decimals can be 0.23, 0.333… etc

Integers are of three types negative numbers like -1, -2 .. , zero and positive numbers like 1, 2, 3…

The negative numbers and zero are called non positive and zero and positive numbers are called non negative numbers.

Decimal numbers are of finite or terminating decimal types or infinite decimal types. The infinite decimal type is classified as rational numbers if they can be expressed in the form p / q or irrational number if they can’t be expressed in the for

Properties:

- The remainder on division of a prime number p > = 5 by 6 is 1 / 5.

2. The remainder of the division of a square of a prime number p > = 5 by 12 / 24 is 1.

3. If a and b are odd prime numbers a2 – b2 and a2 + b2 is composite.

HCF of ‘x’ and ‘y’ is G then HCF of x , (x+y) and x , (x-y) and (x+y) , (x-y) is also G.