business mathematics

Introduction:

Natural Numbers:

All positive integers are natural numbers.
Ex 1,2,3,4,8,......

There are infinite natural numbers and number 1 is the least natural number.
Based on divisibility there would be two types of natural numbers. They are

Prime and composite.

Prime Numbers:

A natural number larger than unity is a prime number if it
does not have other divisors except for itself and unity.
Note:-Unity i e,1 is not a prime number.

Properties Of Prime Numbers:

->The lowest prime number is 2.
->2 is also the only even prime number.
->The lowest odd prime number is 3.
->The remainder when a prime number p>=5 s divided by 6 is 1 or 5.However,
if a number on being divided by 6 gives a remainder 1 or 5 need not be
prime.
->The remainder of division of the square of a prime number p>=5 divide by
24 is 1.
->For prime numbers p>3, p²-1 is divided by 24.
->If a and b are any 2 odd primes then a²-b² is composite. Also a²+b²
is composite.
->The remainder of the division of the square of a prime number p>=5
divided by 12 is 1.

Process to Check A Number s Prime or not:

Take the square root of the number.
Round of the square root to the next highest integer call this number as Z.
Check for divisibility of the number N by all prime numbers below Z. If
there is no numbers below the value of Z which divides N then the number
will be prime.

Example 239 is prime or not?
√239 lies between 15 or 16.Hence take the value of Z=16.
Prime numbers less than 16 are 2,3,5,7,11 and 13.
239 is not divisible by any of these. Hence we can conclude that 239
is a prime number.


Composite Numbers:

The numbers which are not prime are known as composite numbers.

Co-Primes:

Two numbers a an b are said to be co-primes,if their H.C.F is 1.
Example (2,3),(4,5),(7,9),(8,11).....
Place value or Local value of a digit in a Number:

place value:

Example 689745132
Place value of 2 is (2*1)=2
Place value of 3 is (3*10)=30 and so on.
Face value:-It is the value of the digit itself at whatever
place it may be.

Example 689745132
Face value of 2 is 2.
Face value of 3 is 3 and so on.