Question

If $3$ is the least prime factor of number $a$ and $7$ is the least prime factor of number $b$,then the least prime factor of $a+b$ is

• A. $2$
• B. $3$
• C. $5$
• D. $10$

Answer 1

The correct option is A

$2$

Explanation for correct option

$3$ is the least prime factor of number $a$ and $7$ is the least prime factor of number $b$

So , $a$ should be greater than or equal to $3$ and $b$ should be greater than or equal to $7$

Now, consider the case $a=3$ and $b=7$ . Then,

$a+b=3+7$

Therefore $a+b=10$

We know that $2$ is the least prime factor of $a+b$

Let us consider the case $a=3^2=9$ and $b=7^2=49$

It is clear that $a+b=58$ (Even number)

Similarly, for the value of $n$, $a^n+b^n$ is divisible by $2$

So the least prime factor of $a+b$is $2$

Hence option (A) is correct