Question

Write all the prime numbers between:
10 and 40

Answer 1

Hint: We solve this problem by using the definition of a prime number. A prime number is defined as a number which has only two factors that are 1 and itself.
We use the condition that all the prime numbers are odd numbers except 2.
For checking the factors we use the divisibility rules they are
(1) The divisibility rule of says that every number is divisible by 1
(2) The divisibility rule of 2 says that if the unit digit of number is even then that number is divisible by 2
(3) If the sum of digits is equal to multiple of 3 then the number is divisible by 3
(4) If the number formed from last two digits of a number is divisible by 4 then the whole number is divisible by 4
(5) If the unit digit is 0, 5 then the number is divisible by 5
So, we check the definition of all odd numbers that lie between 10 and 40 to take out the prime numbers from those odd numbers between 10 and 40.

Complete step by step answer:
We are asked to list out all the prime numbers between 10 and 40.
We know that the condition that all the prime numbers are odd numbers except 2.
So, let us write down all the odd numbers that are present between 10 and 40 then we get
11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39
Here, we can see that all the numbers are odd numbers which are not divisible by 2.
So, let us check the divisibility with 3
We know that if the sum of digit of a number is a multiple of three then the number of divisible by 3
By using this divisibility rule of 3 we get the numbers that are divisible by 3 between 10 and 40 as
15, 21, 27, 33, 39
We know that if a number has a factor other than 1 and itself is not a prime number.
Now, let us remove the numbers that are divisible by 3 from the list we have then we get
11, 13, 17, 19, 23, 25, 29, 31, 35, 37
Now, let us check the divisibility by 5
We know that if the unit digit is 0 or 5 then the number is divisible by 5
By using the above rule we get the numbers that are divisible by 5 as
25, 35
By removing the numbers that are divisible by 5 from the list we get
11, 13, 17, 19, 13, 19, 31, 37
Here, we can see that the numbers in the above list are all having only two factors that are 1 and itself.
So, we can directly conclude that the list of numbers that are remaining are all prime numbers.

Therefore, we can say that the prime numbers between 10 and 40 are
11, 13, 17, 19, 13, 19, 31, 37

Note: We can solve this problem in other method by checking the factors of each and every numbers starting from 11 to 39
But in this process we need to check all divisibility rules for each and every number that takes so much space and time to find the answer.
So, we go for deleting the numbers that are divisible by other numbers rather than 1 and itself so as to list out the numbers which are prime easily.