Question

The sum of prime numbers between 90 and 100 is?

Answer 1

Hint: We can observe which of the numbers lying between 90 and 100 are prime i.e. have only two factors 1, and itself. The sum of these numbers will give us the required answer. We can use divisibility rules of 2, 3 and 5 in order to check the divisibility by these numbers. If an even digit is placed in one place, then the number is divisible by 2. If the sum of digits is divisible by 3 the number is also divisible by 3. The numbers with 5 at ones place are divisible by 5

Complete step-by-step answer:
Prime numbers: The numbers whose factors are only 1 and itself are called prime numbers. These are the numbers which are not divisible by other numbers such as 2, 3, 5 etc.
The numbers that have an even digit at one’s place will be divisible by 2 and those whose sum of digits is divisible by 3 are also divisible by 3. The numbers with 5 at ones place are divisible by 5
Evaluating the numbers between 90 and 100 for their factors:
 $ \Rightarrow 91 = 13 \times 7$
92 : It has an even number on the one's place and thus will be divisible by 2.
$ \Rightarrow 92 = 2 \times 46$
93 : The sum of its digits is $12(9 + 3)$ which is divisible by 3, so it will also be divisible by 3.
 $ \Rightarrow 93 = 3 \times 31$
94 : It has an even number on the one's place and thus will be divisible by 2.
$ \Rightarrow 94 = 2 \times 47$
95 : It has 5 at its ones place and thus is divisible by 5
$ \Rightarrow 95 = 5 \times 19$
96 : It has an even number on the one's place and thus will be divisible by 2.
$ \Rightarrow 96 = 2 \times 48$
$ \Rightarrow 97 = 97 \times 1$
98 : It has an even number on the one's place and thus will be divisible by 2.
$ \Rightarrow 98 = 2 \times 49$
99 : The sum of its digits is $18(9 + 9)$ which is divisible by 3, so it will also be divisible by 3.
 $ \Rightarrow 99 = 3 \times 33$
The only number between 90 and 100 that has only two factors i.e. 1 and the number itself is 97.
Therefore, the sum of prime numbers between 90 and 100 will also be equal to 97.
So, the correct answer is “97”.

Note: There is no such defined formula to find prime numbers for any range. The use of divisibility rules makes the work easier. Prime numbers are generally odd except 2, 2 is the only prime number. If the number is even, it will surely be divisible by 2 and thus will not satisfy the condition of being a prime number. The other numbers that have more than two factors are known as composite numbers. Factors are those numbers by the product of which the original number is obtained.