Question

What are the prime numbers between 1 to 50?

Answer 1

Hint: There are odd and even numbers between 1 to 50. We know that prime numbers are those numbers that re divisible by 1 and itself. There is no need to check the even numbers because it has 2 as one of the factors along with 1 and itself. Now, divide the given range that is 1 to 50 into sub-ranges like 1 to 10, 10 to 20, 20 to 30, 30 to 40, and 40 to 50. Then, check for prime numbers between every sub-ranges. Solve it further and get all the prime numbers between 1 to 50.

Complete step by step answer:
According to the question, it is asked to find the prime numbers between 1 to 50.
We know that prime numbers are those numbers that are divisible by 1 and itself.
We need to check every number from 1 to 50 whether the number is prime or not.
1 and 2 are also a prime number because it fulfills the definition of the prime number ………………………………….(1)
There is no need to check the even numbers because it has 2 as one of the factors along with 1 and itself. So, we only have to check the odd numbers whether it is prime or not.
The odd numbers between 1 to 10 are 1, 3, 5, 7, and 9.
9 is not a prime number because it has 3 as one of the factors along with 1 and itself.
The prime numbers between 1 and 10, are 1, 2, 3, 5, and 7 ……………………………………..(2)
The odd numbers between 10 to 20 are 11, 13, 15, 17, and 19.
We can observe that 15 is also not a prime number because it has 3 and 5 as its factors along with 1 and itself.
The prime numbers between 10 and 20, are 11, 13, 17, and 19 ……………………………………………(3)
The odd numbers between 20 to 30 are 21, 23, 25, 27, and 29.
We can observe that 21 is also not a prime number because it has 3 and 7 as its factors along with 1 and itself.
Similarly, we can also observe that 25 is also not a prime number because it has 5 as one of its factors along with 1 and itself.
Similarly, we can also observe that 27 is also not a prime number because it has 3 and 9 as its factors along with 1 and itself.
The prime numbers between 20 and 30, are 23 and 29 …………………………………………….(4)
The odd numbers between 30 to 40 are 31, 33, 35, 37, and 39.
Similarly, since 33 has 1,3,11 and 33 as its factors so, 33 is not a prime number.
Similarly, we can observe that 35 and 39 are not a prime number because it has factors other than 1 and itself.
The prime numbers between 30 and 40 are 31, and 37 ………………………………………………….(5)
The odd numbers between 40 to 50 are 41, 43, 45, 47, and 49.
The numbers 45 and 49 are also not a prime number because it has factors other than 1 and itself.
The prime numbers between 40 and 50 are 41,43, and 47 …………………………………………….(6)
From equation (1), equation (2), equation (3), equation (4), equation (5), and equation (6), we have the prime numbers between 1 and 50.
Therefore, the prime numbers between 1 to 50 are 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.

Note:
 The best way to solve this type of question where we have to find the prime numbers between two numbers is, divide the given range of numbers into sub-ranges and then check the numbers whether they are prime or not. Directly finding the prime numbers may lead to missing of some prime numbers by mistake. For instance, in this question, we have divided our range of 1 to 50 into sub-ranges like 1 to 10, 10 to 20, 20 to 30, 30 to 40, and 40 to 50. Then, check for the prime numbers between every sub-ranges.