Question

What is the percentage of prime numbers from \[1\] to \[10\].

Answer 1

Hint: First we have to remember which numbers are the prime numbers . Prime numbers are the numbers which are not divisible by any other numbers except \[1\] and the number itself . So we can say prime numbers have a total of \[2\] factors .We will check all the numbers between \[1\] and \[10\] to know which numbers are prime numbers . Then we will count them . There are total \[10\] numbers between \[1\] and \[10\]. So we will divide the number of prime numbers between \[1\] and \[10\] by \[10\] and multiply it by \[100\] to get the percentage of prime numbers from \[1\] to \[10\].
FORMULA USED :
\[\dfrac{{total\,\,prime\,numbers\,between\,1\,and\,10}}{{10}} \times 100\,\]%

Complete step by step solution:
The numbers from \[1\] to \[10\] are \[1\] , \[2\] , \[3\] , \[4\] , \[5\] , \[6\] , \[7\] , \[8\] , \[9\] , \[10\] .
\[1\] is not a prime number . It has only one factor .
\[2\] is a prime number . It has two factors \[1\] and itself.
\[3\] is a prime number . It has two factors \[1\] and itself.
\[4\] is not a prime factor . It has three factors \[1\],\[2\]and itself.
\[5\] is a prime number . It has two factors \[1\] and itself.
\[6\] is not a prime factor . It has three factors \[1\] , \[2\] , \[3\]and itself.
\[7\] is a prime number . It has two factors \[1\] and itself.
\[8\] is not a prime factor . It has three factors \[1\] , \[2\] ,\[4\]and itself.
\[9\] is not a prime factor . It has three factors \[1\] , \[3\]and itself.
\[10\] is not a prime factor . It has three factors \[1\] , \[2\] , \[5\]and itself.
So we get total \[4\] prime numbers between \[1\] and \[10\]. They are \[2\] , \[3\] , \[5\] , \[7\].
percentage of prime numbers from \[1\] to \[10\]
=\[\dfrac{4}{{10}} \times 100\,\]%
=\[40\]%
percentage of prime numbers from \[1\] to \[10\]= \[40\]%
This is our answer.
So, the correct answer is “40%”.

Note: Not all odd numbers are prime numbers .Some odd numbers can have more than two factors .
\[1\] is not a prime number . It has only one factor . All even numbers except \[2\] are not prime numbers . As they will have a minimum of three factors as every even number is divisible by \[2\] .