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How many prime number are between 10 and 30...?

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Answer
    6
Explanation

Be careful about the above statement "How many prime number are between 10 and 30" mean we have count the prime number between 10 and 30. First of all let us see the defination of Prime Number.

What is a Prime Number?

A number is greater than 1 is called a prime number, if it has only two factors, 1 and the number itself i.e 2, 3, 5, 7, 11 ... also notice that prime number are start form 2.

Now we find Prime Number between 10 and 30?

The number between 10 and 30 are (10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30). They are total 21. We solve this question by Math Shortcut divisible by prime number method. In this method we need to divided the required number by just prime number (2, 3, 5, 7, 11...)

By dividing 2 even number will be omitted only odd number (11, 13, 15, 17, 19, 21, 23, 25, 27, 29) will left for further checking.

By dividing 3 the number (15, 21, 27) will be omitted only odd number (11, 13, 17, 19, 23, 25, 29) will left for further checking.

By dividing 5 the number (25) will be omitted only odd number (11, 13, 17, 19, 23, 29) will left for further checking.

By dividing 7 we understand that no remaining number is divisible by 7. We know about the Prime Number Shortcut by Square root. We know square root of 30 is 5.47 so we required to divide by less then 5.47 i.e 5. We tried by dividing 7 but no remaing number is divible by 7. No need to check further divide and prime number are (11, 13, 17, 19, 23, 29). They are total six (6).

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