Question

Write all prime numbers between: 80 and 100

Answer 1

Hint: Prime numbers basically are the numbers that have only two numbers as their factors (by the product of which they are formed). So, we can write down all the numbers lying between the given range and observe which of them satisfies the condition of being prime. These numbers will be our required answer.

Complete step-by-step answer:
By observing the factors of all the numbers between 80 and 100, we can find which of them are prime.
The numbers which are divisible by 1 and themselves are referred to as prime numbers.
These are the numbers who does not have more than two factors (except 1 and the number).
Factors are the numbers by the product of which the original number is obtained.
Factors for the numbers between 80 and 100 are given as:
 $
  81 \to 3 \times 3 \times 3 \times 3 \\
  82 \to 2 \times 41 \\
  83 \to 1 \times 83 \\
  84 \to 2 \times 2 \times 3 \times 7 \\
  85 \to 5 \times 17 \\
  86 \to 2 \times 43 \\
  87 \to 3 \times 29 \\
  88 \to 2 \times 2 \times 2 \times 11 \\
  89 \to 1 \times 89 \\
  90 \to 2 \times 5 \times 3 \times 3 \\
  91 \to 7 \times 13 \\
  92 \to 2 \times 2 \times 23 \\
  93 \to 3 \times 31 \\
  94 \to 2 \times 47 \\
  95 \to 5 \times 19 \\
  96 \to 2 \times 2 \times 2 \times 2 \times 2 \times 3 \\
  97 \to 1 \times 97 \\
  98 \to 2 \times 7 \times 7 \\
  99 \to 3 \times 3 \times 11 \\
  $
The only numbers with 2 factors i.e. 1 and the number itself are 83, 89 and 97.
Therefore, the prime numbers between 80 and 100 are 83, 89 and 97.
So, the correct answer is “ 83, 89 and 97”.

Note: Instead of writing down all the factors of the numbers lying in the given range, we can use divisibility rules of various numbers. As prime factors will not have other factors except 1 and itself, then they should not satisfy any divisibility rule. For example:
Any number with even digits at its one place will be divisible by 2. E.g. 94, 92, etc. will be divisible by 2 and thus will not be prime.
If the sum of the digits of the number is divisible by 3, then the number will also be divisible by 3. E.g. the sum of digits in 93 is 12 which is divisible by 3, so 936 will also be divisible by 3 and thus will not be a prime number.
Any number with 5 or 0 at its one place will be divisible by 5. E.g. 95, 90, etc. will be divisible by 5 and thus will not be prime.