Question

Which of the following is a prime number?
$
  \left( a \right)19 \\
  \left( b \right)20 \\
  \left( c \right)21 \\
  \left( d \right)22 \\
$

Answer 1

Hint-In this question, we use the concept of prime number. Prime numbers are the positive integers having only two factors, 1 and the integer itself. For example, factors of 6 are 1, 2, 3 and 6, which are four factors in total. But factors of 7 are only 1 and 7, totally two. Hence, 7 is a prime number but 6 is not a prime number.

Complete step-by-step solution -
Now, we have to factorize the following option one by one. If any option has only two factors 1 and the integer itself So, that option is prime number.
First option, 19
Now the factories 19,
\[19 = 1 \times 19\]
 We can see that 19 has only two factors 1 and itself 19. So, 19 is the prime number.
Second option, 20
Now the factories 20,
\[20 = 1 \times 2 \times 2 \times 5\]
We can see 20 has two factors (2 and 5) other than 1 and itself 20. So, 20 is not a prime number.

Third option, 21
Now the factories 21,
\[21 = 1 \times 3 \times 7\]
We can see 21 has two factors (3 and 7) other than 1 and itself 21. So, 21 is not a prime number.
Fourth option, 22
Now the factories 22,
\[22 = 1 \times 2 \times 11\]
We can see 22 has two factors (2 and 11) other than 1 and itself 21. So, 22 is not a prime number.
So, the correct option is (a).

Note-In such types of problems we have to factory the given number into the simplest form but sometimes it is difficult to factorize into the simplest form. So, we can use the divisibility rules. Like the Divisibility rule of 2 is any number ends with 0, 2,4,6,8 so that number is divisible by 2. Divisibility rule of 3 is the sum of digits of any number is divisible by 3. So, we can use the Divisibility rule of 2, 3, and 5 and so on.