Question

The number of prime numbers between $0$ and $20$ is
A. $7$
B. $8$
C. $6$
D. $9$

Answer 1

Hint: For this problem we will write factors of each number from $0$ to $20$. From those factors we will calculate the number of prime numbers from $0$ to $20$ as we know that a Prime number is a number that has only two factors, the first factor is One and the second factor is the number itself.

Complete step-by-step solution:
The factors of the numbers from $0$ to $20$ as follows
We can write $2$ as
$2=1\times 2$
Hence the factors of $2$ are $1$ and $2$.
We can write $3$ as
$3=1\times 3$
Hence the factors of $3$ are $1$ and $3$.
We can write $4$ as
$4=2\times 2$
Hence the factors of $4$ are $2$.
We can write $5$ as
$5=1\times 5$
Hence the factors of $5$ are $1$ and $5$.
We can write $6$as
$6=2\times 3$
Hence the factors of $6$ are $2$ and $3$.
We can write $7$ as
$7=1\times 7$
Hence the factors of $7$ are $1$ and $7$.
We can write $8$ as
$8=4\times 2=2\times 2\times 2$
Hence the factors of $8$ are $2$and $4$.
We can write $9$ as
$9=3\times 3$
Hence the factor of $9$ is $3$.
We can write $10$ as
$10=2\times 5$
Hence the factors of $10$ are $2$ and $5$.
We can write $11$ as
$11=1\times 11$
Hence the factors of $11$ are $1$ and $11$.
We can write $12$ as
$12=2\times 6=2\times 2\times 3$
Hence the factors of $12$ are $2,3,6$.
We can write $13$ as
$13=1\times 13$
Hence the factors of $13$ are $1$ and $13$.
We can write $14$ as
$14=2\times 7$
Hence the factors of $14$ are $2$ and $7$.
We can write $15$ as
$15=3\times 5$
Hence the factors of $15$ are $3$ and $5$.
We can write $16$ as
$16=2\times 8=2\times 2\times 4=2\times 2\times 2\times 2$
Hence the factors of $16$ are $2,4,8$.
We can write $17$ as
$17=1\times 17$
Hence the factors of $17$ are $1$ and $17$.
We can write $18$ as
$18=2\times 9=2\times 3\times 3$
Hence the factors of $18$ are $2,3,6,9$.
We can write $19$ as
$19=1\times 19$
Hence the factors of $19$ are $1$ and $19$.
We can write $20$ as
$20=2\times 10=2\times 2\times 5$
Hence the factors of $20$ are $2,4,5,10$.
From the above values, the numbers that have only two factors and also the two factors are One and the number itself are $2,3,5,7,11,13,17,19$. Hence the number of prime numbers from $0$ to $20$ is $8$.

Note: 1 is not a prime number. So don’t consider that One as a prime number and the number of prime numbers from $0$ to $20$ is $9$. You can also check the condition of the prime number by checking that the number is divisible by any number from $2$ to $10$. If it is divisible by any number from $2$ to $10$, then it must have more than two factors. You can write $1$ as a factor for all the numbers that won’t matter.