Question

What are the prime numbers? List all the primes between 1 to 30.

Answer 1

Hint: Use the definition of numbers and its types. Then from definition of Natural numbers divide it into prime and composite. By the definitions of primes and composite divide the list of numbers from 1 to 30 into 2 groups. Take the list of primes and show it as the result.

Complete step-by-step answer:
Numbers:
A number is a mathematical object or thought which is used to count, measure and represent. Types of numbers possible are natural numbers, whole numbers, integers, rational numbers, irrational.
Natural Numbers:
The numbers greater than 0, starting from 1 and ranging till infinity are called as Natural numbers.
Whole numbers:
The set which contains all the natural numbers from 1 to infinity including the term 0 is called whole numbers.
Integers:
The set containing the negative numbers with all the whole numbers is called Integer.
Rational numbers:
The numbers in the form of $\dfrac{p}{q}$ where q is not equal 0 and p, q are in their lowest terms.
Prime Numbers:
A prime number is a natural number greater than 1 that is not a product of 2 smaller natural numbers. It will have only 2 factors: 1 and itself.
Composite Numbers:
A composite number is a natural number greater than 1 that is possible to break into 2 smaller natural numbers. It will have more than 2 factors. It is also said the natural number which is not prime is composite.
The prime and composite numbers from 1 to 30 are given below.
1 – composite; 2 – prime; 3 – prime; 4 – composite; 5 – prime; 6 – composite; 7 – prime; 8 – composite; 9 – composite; 10 – composite; 11 – prime; 12 – composite; 13 – prime; 14 – composite; 15 – composite; 16 – composite; 17 – prime; 18 – composite; 19 – prime; 20 – composite; 21 – composite; 22 – composite; 23 – prime; 24 – composite; 25 – composite; 26 – composite; 27 – composite; 28 – composite; 29 – prime; 30 – composite
From the above list we can take all prime numbers.
Let the name of the set be as k.
$k=\left\{ 2,3,5,7,11,13,17,19,23,29 \right\}$
The list above are all the prime numbers from 1 to 30.
Hence, listed all primes.

Note: While denoting a number to be composite be sure that you have a number which will divide the number you have. This is done to prove that it has a factor other than 1 and number itself. Then only you will get the correct value.