Question

The difference between the number of numbers from 2 to 100 which are not divisible by any other number except and itself and the numbers which are divisible by at least one more number along with one and itself.
A) 25
B) 50
C) 49
D) None of these

Answer 1

Hint:
The numbers which are not divisible by any other numbers except one and itself are called prime numbers and the numbers which are divisible by at least one more number along with one and itself are called composite numbers. That means here we need to find the difference between the number of prime numbers and number of composite numbers between 2 and 200.

Complete step by step solution:
There are a total of 99 numbers from 2 to 100.
Here we have to find the numbers of composite and prime numbers between 2 to 100.
Now, we will first find the number of prime numbers from 2 to 100.
Number of prime numbers from 2 to 100 is 25.
 2, 3, 5, 7, 11, ……… , 83, 89, 97 are prime numbers from 2 to 100.
If we subtract the total number of prime numbers from the total numbers, we will get the composite numbers.
Therefore, total number of composite numbers \[ = 99 - 25 = 74\]
We need to find the difference between the number of prime numbers and number of composite numbers.
Therefore, required difference \[ = 74 - 25 = 49\]

Hence, the correct option is option C.

Note:
Here, we have to read the question carefully to understand what needs to be found out. It is also important to know the definition of prime and composite numbers. Prime numbers have only 2 factors whereas composite numbers have more than two factors. If we have to count numbers from 2 to 100, then we have to include 2 and 100 as well. 1 is neither a prime nor a composite number and 2 is the only even number which is prime.