Find the total number of prime numbers between 1 and 50 including both
The correct answer and explanation is:
The prime numbers between 1 and 50 are the numbers that are greater than 1 and have no divisors other than 1 and themselves. These are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
Now let’s count these prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
There are 15 prime numbers between 1 and 50.
Explanation:
Prime numbers are defined as natural numbers greater than 1 that cannot be divided by any other numbers except for 1 and the number itself. For example:
- 2 is prime because its only divisors are 1 and 2.
- 3 is prime because its only divisors are 1 and 3.
- 4 is not prime because it is divisible by 1, 2, and 4.
The process of identifying prime numbers involves testing each number between 1 and 50 to see if it has any divisors other than 1 and itself. For example, 9 is not prime because it is divisible by 3 (9 = 3 × 3). Similarly, 25 is not prime because it is divisible by 5 (25 = 5 × 5).
There is only one even prime number, which is 2. All other even numbers can be divided by 2, so they are not prime. For larger numbers, checking divisibility by prime numbers smaller than the square root of the number can help confirm whether a number is prime.
Thus, after systematically checking each number, the list of prime numbers between 1 and 50 includes 15 prime numbers in total.