Question

Write the first prime numbers.

Answer 1

Hint: First of all, recall that the definition of prime numbers is the numbers which have only two factors. Now, start factorising the numbers from 1 and find the first five such numbers which have only two factors.

Complete step-by-step answer:
Here, we have to find the first five prime numbers.
Now, we know that prime numbers are numbers that are not composite, that is the numbers which have only two factors.
Let us start writing the factors of numbers starting from 1.
$1 = 1 \times 1$
We can see that 1 has only one factor. Therefore, 1 is not a prime number.
Here, 2 can be factorised as $2 \times 1$, that is, 2 have only two factors, 2 and 1 and hence our first prime number.
Similarly, 3 can be factorised as $3 \times 1$, means 3 has only two factors, 3 and 1, hence, 3 is a prime number.
Next, 4 is divisible by 2,4 and 1. Therefore, it has now than 2 factors and hence, not a prime number.
Also, 5 is divisible only by 1 and 5. Hence, 5 is also a prime number.
Next, 6 is divisible by 2,3,6 and 1. Therefore, 6 is a composite number and not a prime number.
But, 7 has only 2 factors, 7 and 1. Hence, 7 is a prime number.
We can see that, 8 has 4 factors, 1,2,4 and 8.
The number 9 has 3 factors, 1,3 and 9. So, 9 is not a prime number.
Also, 10 is divisible by 1,2,5 and 10 and have more than 2 factors. Hence, 10 is not a prime number.
 Whereas, 11 has only two factors 1 and 11. Hence, 11 is also a prime number.
Therefore, the first five numbers are 2,3,5,7 and 11.

Note:- Students must note that all odd numbers are not considered as prime numbers. For example, 9 is an odd number but not a prime number. Prime numbers are numbers which have only two factors, 1 and the number itself. Hence, find the factors of each number and then decide whether it is a prime number or not.