Question

If a and b are two positive integers such that the least prime factor of a is $3$ and the least prime factor of b is $5$. Then, calculate the least prime factor of $\left( {a + b} \right)$.

Answer 1

Hint: The given questions involve some basic concepts and techniques of number system analysis. The question can be solved easily if we pay attention to the details of the questions and try to solve the problem with a strategy.

Complete step-by-step answer:
In the given question, we are given two positive integers a and b with some conditions on them. So, we are given that the least prime factor of a is $3$ and the least factor of b is $5$. So, we are required to calculate the least prime factor of sum of the two positive integers given to us.
Hence, the least prime factor of the positive integer a is $3$. So, this means that $2$ is not a prime factor of a. Hence, we can conclude that the positive integer a is odd.
Also, we are given that the least prime factor of the positive integer b is $5$. So, this means that $2$ is not a prime factor of b. Hence, we can conclude that the positive integer b is also odd.
Now, we know that both the positive integers a and b given to us are odd positive integers. So, we have to calculate the least prime factor of $\left( {a + b} \right)$.
We know that the sum of two odd positive integers is even. Hence, we get the sum of the positive odd integers a and b as an even integer. We also know that every even integer is divisible by $2$. Moreover, $2$ is the least prime number. So, we get the least prime factor of $\left( {a + b} \right)$ as $2$.
So, the correct answer is “2”.

Note: The question tests our analytical and comprehensive abilities of mathematics as a subject. One must be familiar with the concepts of number system and divisibility in order to understand such questions and solve the given problem.