PRIME NUMBERS AND THE NUMBER LINE

Every composite number can be expressed as a product of primes, and this factorization is unique, regardless of the  order in which the prime factors occurs.A prime number is a natural number which is not divisible by any other number except 1 and itself..So, 2, 3, 5, 7, 11, 13, 17,1 9,23 etc... are prime numbers.

A composite number  is any natural number divisible by any other number besides 1 and itself. So, 4, 6, 8, 9, 10, 12, 15, 16, ....etc. are composite numbers.

The Primality test
Let n be any natural number. To establish establish whether n is a prime or not the following steps are taken.
 

Step 1 : Find approximate square root of the  given number.

Step 2 : Divide the given number by prime numbers less than approximate square root of number. If given number is not divisible by any of these prime numbers, the number is a prime else it’s a composite.

Ex. Is 37 it a prime number ?

Sol.

Let n=37

Step 1 :  √n=√37 = 6.08 ≈ 7

Step 2 : Prime numbers < 7 are 2,3, and 5  all do not evenly divide 37. so, 37 is a prime number.


NUMBER LINE

INTEGERS ON A NUMBER LINE
Integers can be represented by points on a straight line known as the number line. For this, a straight line that extends infinitely in both directions(left and right) is drawn. A point O called the origin is marked on to the line, and points 1, 2, 3, 4…  and points -1, -2, -3, -4,…. are marked on the right and left hand side respectively of point O as shown in the figure below.

In this way, each positive integer is a point on the right hand side of point O and each negative integer is a point on the left hand side of point O on the number line.



RATIONAL NUMBERS ON A NUMBER LINE

By the same token, rational numbers can be represente as shown below