Question

Consider the following numbers.
1. 247
2. 203
Which of the following is/are prime?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2

Answer 1

Hint:First, before proceeding for this, we must know that a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. Then, starting with the first number which is 247, we should know that it should not get divided by any further till its half of the number. Then, similarly we check for the number 203 whether it gets divided by any prime number or not and gets the final conclusion.

Complete step-by-step answer:
In this question, we are supposed to find whether the given numbers which are 247 and 203 are prime numbers or not.
So, before proceeding for this, we must know that a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.
Moreover, a natural number greater than 1 which is not a prime number is called a composite number.
Now, starting with the first number which is 247, we should know that it should not get divided by any further till its half of the number.
So, we should use the series of the prime numbers to check whether the given number is prime or not by dividing it with those numbers.
So, the series of the prime numbers is 2, 3, 5, 7, 11, 13, 17, 23, 29 and so on.
Now, usually the number gets divided by the prime numbers from the above range and we need not go further for checking.
Then, we can see clearly that 247 gets divided by the number 13 as:
$\dfrac{247}{13}=19$
So, 247 is not a prime number.
Similarly, now we check for the second number which is 203.
Now, for that also, we can see clearly that it gets divided by 7 as:
$\dfrac{203}{7}=29$
So, 203 is also not a prime number.
So, we get the conclusion that neither first number nor second number is prime.
Hence, option (d) is correct.

Note: Now, to solve these types of the questions we need to know some of the basic facts about the prime numbers. So, the most important fact about prime numbers is that 2 is the smallest prime number and moreover it is the only even prime number.