Question

Which number should be added to $195$ so that it becomes prime?

Answer 1

Hint: It should be clear that we have to add the smallest number to make it prime. Otherwise, there would be no sense of doing it. We have to add one by one starting from $1$ to get a prime number. Prime numbers are those numbers which are divisible by $1$ and itself only.

Complete step-by-step answer:
A prime number is that number which can be divided by $1$ and itself only.
In the given question, we have $195$ which is a composite number. A composite number is that number which can be divided by other than $1$ and itself.
So, we have to make it a prime number.
We can do this by adding numbers in it starting from $1$.
If we add$1$ in $195$ , we get $196$.
Now, let’s do the prime factorization of $196$ .
Thus, the prime factorization is \[{\mathbf{2}}{\text{ }} \times {\text{ }}{\mathbf{2}}{\text{ }} \times {\text{ }}{\mathbf{7}}{\text{ }} \times {\text{ }}{\mathbf{7}}{\text{ }} = {\text{ }}{\mathbf{2}}{\;^{\mathbf{2}}}\; \times {\text{ }}{\mathbf{7}}{\;^{\mathbf{2}}}\].
Therefore, we can see that it is divisible by other than $1\,\,and\,\,196$ .
Hence, it is not prime.
Now,
Let’s add $2$ in $195$, and we get $197$.
Now, we have to do the prime factorization of $197$.
Thus, the prime factorization is \[197 = 1 \times 197\].
Therefore, we can easily see that it has only two factors: $1$ and itself.
So, it is a prime number.
Hence, we have to add $2$to $195$ to make it a prime number.
So, the correct answer is “2”.

Note: If we keep on adding in the given number then we will get different prime numbers. Prime factorization is the best method to find whether the number is a prime number or not. There can also be some numbers below $195$ which are prime. To find them we have to do subtraction in a similar manner.