Question

all the prime number between 10 and 40​

Answer 1

Answer:

11,13,17,19,23,29, 31,37

Answer 2

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 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

Now, let us check the divisibility by 5We 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

By using the above rule we get the numbers that are divisible by 5 as25, 35

• By removing the numbers that are divisible by 5

from the list we get

from the list we get11, 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 are11, 13, 17, 19, 13, 19, 31, 37