Tuesday, January 27, 2015

Numbers:in hindu - Arabic system , we have ten digits , namely 0,1,2,3,4,5,6,7,8,9
Called zero,one,two,three,four,five,six,seven,eight,and nine respectively.
Numeral: A number is denoted by a group of digit , called numeral .
For denoting a numeral ,we use the place - value chart .
2. Face value : The face value of a digit in a numeral is its own value , at whatever place it may be . example
In the numeral 58932
The face value of  9 is 9
The face value of 2 is 2.

3. Types of Numbers :
a. Natural Numbers
b.Whole Numbers
c.Integers

4. Even And Odd Numbers :

5; prime Numbers : A counting number is called a prime number if it has exactly two factors namely itself and 1 that is prime number are divided by 1 and itself ,  not any other number.
All prime number less than 100 are:
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97.

Test For a Number to be primes :
Let p be a given number  and let n be the smallest counting number such that (n×n) greater than equal to p {(n×n)>=p} .
Now test whether p is divisible by any of the prime number less than or equal to n.
Example : (1) test which of the following are prime numbers?
(A) 61
Solution : Step (A.1)
choose a number whose square is greater than the given number (like in this question 61)
The closest number n= 8
Step(A.2):  now square of 8 is
n×n = 8×8= 64
which is greater than 61

Step (A.3) : prime number less than 8 is 2,3,5,7
Step (A.4) : now 61 is divided by  these numbers  we see that none of them divides 61
Hence 61 is a prime number

(B) : 173
n = 14
14×14 = 196 which is greater than 173
Prime numbers less than 14 is 2,3,5,7,11,13
Clearly , non of them divides 173
Hence it is a prime number

(C) : 321
n = 18
18×18 = 324, which is greater than 321
Prime numbers less than 18 are 2,3,5,7,11,13,17,
We see that 3 divides 321 hence 321 is not a prime number .
Other questions are
(D): 437, 137 , 991 etc .


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