Question

Find the range of the first seven prime numbers.

Answer 1

Hint: To solve this question we need to have a knowledge of prime numbers and range for a set of numbers. Prime numbers are the numbers which have two factors, one is the number itself while other is$1$. Range is the difference between the highest and the lowest values present in a set of numbers. In this case the set of numbers contains the first seven prime numbers.

Complete step by step answer:
The question asks us to find the range of the first seven prime numbers. To find this we will firstly find the first seven prime numbers. So the first seven prime numbers are $2,3,5,7,11,13$and $17$.
Now we will consider these numbers as a set which contains the first seven prime numbers, so the range will be the difference of the highest and the lowest numbers in the set. The highest and lowest prime numbers which are subtracted are $17$and $2$ respectively. So the range in mathematical form will be written as:
$\Rightarrow \text{Range}=\text{Highest term-Lowest term}$
In the case of this question the highest term and the lowest term are seventh term and first term respectively.
$\Rightarrow \text{Range =}{{\text{7}}^{\text{th}}}\text{term-}{{\text{1}}^{\text{st}}}\text{term}$
On substituting the values we get in the above expression we get:
$\Rightarrow \text{Range}=17-2$
On subtracting the number we get:
$\Rightarrow \text{Range}=15$
$\therefore $ The range of the first seven prime numbers is $15$.

Note: We can check whether the numbers are prime or not. For doing this we will find factors of the numbers. Do remember that $2$ is the only even prime number in the number system. Similarly the first odd prime number is $3$ and not $1$.