Question

The number of primes between 0 and 20 is

(A) 7

(B) 8

(C) 6

(D) 9

Answer 1

Hint: A number whose factors are 1 and itself only is called a prime number.

A prime number is not divisible by any other number than 1 and itself. So, any prime number has only two factors.

Using this definition of prime numbers, we check if the numbers 0 to 20 are primes or not. Then we count the number of prime numbers between 0 and 20, which is the required answer.

Complete step by step answer:

We are asked to find the number of primes between the numbers 0 and 20.

First let us consider the number 0. It is divisible by all the numbers ${\displaystyle \frac{0}{\text{Any number}}}=0$. So, it is not a prime number.

Now let us consider 1. It has only 1 factor, So it is not a prime number.

Now let us consider 2. It has only two factors: $1,2$. So, 2 is a prime number.

Now for the remaining numbers let us divide them into two groups even and odd.

The numbers $4,6,8,10,12,14,16,18$ and $20$ are even numbers. So, all of them are divisible by 2, that is they have more than two factors. So, they are not prime numbers.

The remaining numbers (odd) are 3, 5, 7, 9, 11, 13, 15, 17 and 19.

Among them 9 and 15 are divisible by 3, they have more than 2 factors. So, they are not prime numbers.

The remaining numbers 3, 5, 7, 11, 13, 17 and 19 are not divisible by any numbers other than 1 and themselves. So, they are prime numbers.

$\therefore$ We get that the prime numbers between 0 and 20 are $2,3,5,7,11,13,17$ and $19$. We need the count of these prime numbers. There are eight prime numbers between $0$ and $20$. 

The number of prime numbers between 0 and 20 is $8$. So, the correct answer is “Option B”.

Note: 

> Note that the number $1$ is neither prime nor composite.

• 1 is not a prime number because for a prime number the number should have two divisors 1 and itself. Now, 1 has only one divisor i.e. 1.

• 1 is not a composite number because a number is a composite number when it has a divisor which is not 1 and itself so here 1 has only one divisor i.e. 1.

> $2$ is the only even prime number. Remaining all prime numbers are odd.