Numbers

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 h...ave 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.





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 numberwill 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

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